01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
,
Keywords:
branching theory of nonlinear equations; bifurcation; singular problems; rgularization; approximate methods; differential-operator equations; kinetic systems
Principal investigation concerns the theory of branching solutions of nonlinear equations. The general existence theorems for bifurcation points, curves and surfaces are proved by consideration of the branching equation reduced to the canonical form with the use of combinations of analytical, topological and algebraic methods. The proof method for these theorems intensively uses the Jordan structure of a linearized problem, as well as application of the Kronecker - Poincare Index, the Morse - Conley Index and search of conditional extremum points of the definite functions corresponding to the branching equation. The method is also aplicable in the case of a vector parameter when the bifurcation points of a solution can fill in curves or surfaces. It makes it possible to construct an asymptotics of appropriate solution branches and consider their stability. The general theory is used for a problem of branching solutions of nonlinear elliptic equations classes and applications (e.g. the existence theorems are proved and the asymptotics of solutions of the Karman boundary value problem for systems with a biharmonic operator is constructed, the solutions of integral compensation equation of the theory of superconductivity are constructed, the bifurcation analysis of some problems for kinetic Vlasov-Maxwell systems which describe a behaviour of multicomponent plasma is realized.) The analysis of generating of free parameters in branching solutions of general classes of the nonlinear equations in Banach spaces is carried out on the base of the interlaced branching equations theory, constructed for this purpose. The backgrounds of the theory of iterative methods in a neighborhood of solution branch points of the nonlinear equations in Banach spaces are developed: the method of sequence of successive approximations with an explicit and implicit parametrization of branches, including most general N-stepped iterative method with the explicit indication of uniformization of branching solutions and construction of an initial approximation are offered; the methods of a regularization of calculations in a neighborhood of solution branch points ensuring uniform approximation of branching solutions are given. The basic results in the theory of differential - operator equations (ordinary and in partial derivatives) in Banach spaces with an irreversible operator in the main part are obtained: the existence theorems in linear and nonlinear cases are proved; the methods of reduction of this problem to the ordinary differential equations of the infinite order, to "scalar" integral equations, to the differential equations with a singular point are offered; the method of construction of classic and generalized solutions on the base of a Jordan structure of operator coefficients of a linearized equation is developed. More than 100 articles were published and reviewed (see some abstracts of these articles in Mathematical Review : 87a:58036; 98f:47069; 98d:35221; 96k:65042; 95c:47079; 93m:82047; 93a:47054; 92i:47077; 90m:58033; 89i:45018; 85j:34139; 85b:34072; 82a:47011 etc.)
Biography
Honored Scientist of the Russian Federation.
Graduated from Faculty of Physics and Mathematics Irkutsk State University (ISU) in 1962. Ph.D. thesis was defended in 1967. D.Sc. thesis was defended in 1983.
In 1999 was awarded the sign " Honorable member of Higher Professional Education in Russia". Academician of Academy Sciences of Nonlinear Sciences -1998, Member-Correspondent of Academy Sciences of Higher School of Russia-1999.
Main publications:
N. Sidorov, D. Sidorov, A. Sinitsyn, Toward General Theory of Differential-Operator and Kinetic Models, World Scientific Series on Nonlinear Science Series A, 97, eds. Leon O Chua (University of California at Berkeley, USA), World Scientific Series, Singapore, 2020 , 496 pp
Nikolay Sidorov, Boris Loginov, et al Lyapunov-Schmidt methods in nonlinear analysis and applications, Mathematics and its Applications, 550, Kluwer Academic Publishers, Dordrecht, 2002
L. D. Dreglea Sidorov, N. A. Sidorov, “The Cauchy problem with a parameter perturbed by a linear functional”, Proceedings of the Voronezh international spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV”, Voronezh, April 26-30, 2024, Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 237, VINITI, Moscow, 2024, 10–17
2023
2.
N. A. Sidorov, Lev Ryan D. Dreglea Sidorov, “On the solution of Hammerstein integral equations with loads and bifurcation parameters”, The Bulletin of Irkutsk State University. Series Mathematics, 43 (2023), 78–90
3.
N. A. Sidorov, L. R. D. Dreglea Sidorov, “Analytic Construction of Solutions to Integral Equations with Linear Functionals and Parameters”, Technical Physics, 2023, 9
4.
L. R. D. Dreglya Sidorov, N. A. Sidorov, “Ob odnom klasse nelineinykh uravnenii v bananovykh prostranstvakh s lineinym funktsionalom i parametrom”, Dinamicheskie sistemy i kompyuternye nauki: teoriya i prilozheniya (DYSC 2023) : materialy 5-i Mezhdunarodnoi konferentsii (Irkutsk, 18–23 sentyabrya 2023 g.), eds. A. V. Arguchintsev, Izdatelstvo IGU, 2023, 22–25
5.
L. R. Dreglea Sidorov, N. Sidorov, D. Sidorov, “The linear Fredholm integral equations with functionals and parameters”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2023, no. 2, 83–91;
N. A. Sidorov, “Special Issue Editorial “Solvability of Nonlinear Equations with Parameters: Branching, Regularization, Group Symmetry and Solutions Blow-Up””, Symmetry, 14:2 (2022), 226 , 4 pp. www.mdpi.com/2073-8994/14/2/226
N. A. Sidorov, D. N. Sidorov, “Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters”, Mathematics, 10:12 (2022), 2134 , 14 pp.
S. Noeiaghdam, D. Sidorov, A.-M. Wazwaz, N. Sidorov, V. Sizikov, “The Numerical Validation of the Adomian Decomposition Method for Solving Volterra Integral Equation with Discontinuous Kernels Using the CESTAC Method”, Mathematics, 9:3 (2021), 260 , 15 pp.
N. A. Sidorov, D. N. Sidorov, “Nelineinye uravneniya Volterry s nagruzkami i bifurkatsionnymi parametrami: teoremy suschestvovaniya i postroenie reshenii”, Differentsialnye uravneniya, 2021, 1654–1664
10.
A. Dreglea, N. Sidorov, D. Sidorov, “Construction of solutions of integral equations with Stieltjes functionals and bifurcation parameters”, 2, no. 12, 2021, 7 pp., p.43-49 (Dedicated to the memory of Academician Mitrofan M. Cioban, 1942-2021)
N. A. Sidorov, A. I. Dreglea, D. N. Sidorov, “Generalisation of the Frobenius Formula in the Theory of Block Operators on Normed Spaces”, Mathematics, 9:23 (2021), 3066 , 15 pp.
13.
A. S. Andreev, I. V. Boykov, P. A. Vel'misov, V. Z. Grines, E. V. Desyaev, D. K. Egorova, R. V. Zhalnin, E. B. Kuznetsov, I. V. Lutoshkin, A. G. Lvov, T. Ph. Mamedova, S. M. Muryumin, I. P. Ryazantseva, P. V. Senin, D. N. Sidorov, N. A. Sidorov, L. A. Sukharev, V. F. Tishkin, I. I. Chuchaev, P. A. Shamanaev, “To the 80th anniversary of Vladimir Konstantinovich Gorbunov”, Zhurnal SVMO, 23:2 (2021), 207–210
2020
14.
S. Noeiaghdam, A. Dreglea, J. He, Z. Avazzadeh, M. Suleman, M.A.F. Araghi, D.N. Sidorov, N.A. Sidorov,, “Error estimation of the homotopy perturbation method to solve second kind Volterra integral equations with piecewise smooth kernels: Application of the CADNA library”, Symmetry, 12:10 (2020), 1730 , 16 pp.
N. Sidorov, D. Sidorov, A. Dreglea, “Solvability and bifurcation of solutions of nonlinear equations with Fredholm operator”, Symmetry, 12:6, 920 (2020), 1–21
E.M. Rojas, N.A. Sidorov, A.V. Sinitsyn, “A boundary value problem for noninsulated magnetic regime in a vacuum diode”, Symmetry, 12:4 (2020), 617 , 14 pp.
17.
S. Noeiaghdam, D. Sidorov, V. Sizikov, N. Sidorov, “Control of accuracy on Taylor-collocation method to solve the weakly regular Volterra integral equations of the first kind by using the CESTAC method”, Applied and Computational Mathematics, 19:1 (2020), 87–105link, arXiv: 1811.09802
18.
N. Sidorov, D. Sidorov, A. Sinitsyn, Toward General Theory of Differential-Operator and Kinetic Models, World Scientific Series on Nonlinear Science Series A, 97, eds. Leon O Chua (University of California at Berkeley, USA), World Scientific Series, Singapore, 2020 , 496 pp.
N. A. Sidorov, “The role of a priori estimates in the method of non-local continuation of solution by parameter”, The Bulletin of Irkutsk State University. Series Mathematics, 34 (2020), 67–76
20.
N. A. Sidorov, A. I. Dreglea, “Differential equations in Banach spaces with an irreversible operator in the principal part and nonclassical initial conditions”, Differential Equations and Optimal Control, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 183, VINITI, Moscow, 2020, 120–129
21.
N. A. Sidorov, D. N. Sidorov, A. V. Sinitsyn, “Review of monograph “Toward General Theory of Differential-Operator and Kinetic Models””, The Bulletin of Irkutsk State University. Series Mathematics, 32 (2020), 118–123
2019
22.
N. A. Sidorov, “Classic solutions of boundary value problems for partial differential equations with operator of finite index in the main part of equation”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 55–70
N. Sidorov, D. Sidorov, Y. Li, “Basins of Attraction and Stability of Nonlinear Systems Equilibrium Points”, Differential Equations and Dynamical Systems (Springer), 2019, 09713514 , 14 pp.
N. Sidorov, D. Sidorov, Y. Li, “Nonlinear systems equilibrium points: branching, blow-up and stability”, All-Russian Conference and School for Young Scientists, devoted to 100th Anniversary of Academician L.V. Ovsiannikov on Mathematical Problems of Continuum Mechanics, MPCM 2019 (Technopark of Novosibirsk Akademgorodok, Novosibirsk; Russian Federation; 13 May 2019 through 17 May 2019;), Journal of Physics: Conference Series, 1268:1 (2019), 012065 , 6 pp.
N. A. Sidorov, D. N. Sidorov, Yong Li, “Areas of attraction of equilibrium points of nonlinear systems: stability, branching and blow-up of solutions”, IIGU Ser. Matematika, 23 (2018), 46–63
26.
A. I. Dreglea, N. A. Sidorov, “Integral equations in identification of external force and heat source density dynamics”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 3, 68–77
N. A. Sidorov, O. A. Romanova, M. V. Falaleev, D. N. Sidorov, V. K. Gorbunov, A. I. Dreglea, “In the memory of professor Boris Vladimirovich Loginov”, IIGU Ser. Matematika, 23 (2018), 96–99
2017
28.
A. I. Dreglea, N. A. Sidorov, “The identification of external force dynamics in the modeling of vibration”, IIGU Ser. Matematika, 19 (2017), 105–112
29.
D. N. Sidorov, N. A. Sidorov, “Solution of irregular systems of partial differential equations using skeleton decomposition of linear operators”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:2 (2017), 63–73
N. A. Sidorov, D. N. Sidorov, “Skeleton decomposition of linear operators in the theory of nonregular systems of partial differential equations”, IIGU Ser. Matematika, 20 (2017), 75–95
2016
31.
Leonardo Rendón, Alexandre V. Sinitsyn, Nikolai A. Sidorov, “Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov-Maxwell system”, Rev. Colombiana Mat., 50:1 (2016), 85–107
I. R. Muftahov, D. N. Sidorov, N. A. Sidorov, “Lavrentiev regularization of integral equations of the first kind in the space of continuous functions”, IIGU Ser. Matematika, 15 (2016), 62–77
2015
33.
N. A. Sidorov, D. N. Sidorov, I. R. Muftahov, “Perturbation theory and the Banach–Steinhaus theorem for regularization of the linear equations of the first kind”, IIGU Ser. Matematika, 14 (2015), 82–99
34.
O. A. Romanova, N. A. Sidorov, “On the construction of the trajectory of a dynamical system with initial data on the hyperplanes”, IIGU Ser. Matematika, 12 (2015), 93–105
35.
I. R. Muftahov, D. N. Sidorov, N. A. Sidorov, “On perturbation method for the first kind equations: regularization and application”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:2 (2015), 69–80
N. A. Sidorov, “The chronicle of the Irkutsk regional branch of research-methodological Council on mathematics of the Ministry of Education and Science of the Russian Federation”, IIGU Ser. Matematika, 11 (2015), 106–107
2014
37.
N. A. Sidorov, D. N. Sidorov, “On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels”, Math. Notes, 96:5 (2014), 811–826
2013
38.
N. A. Sidorov, “Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov–Maxwell system”, Izv. Irkutskogo gos. un-ta. Ser. Matematika, 6:4 (2013), 85–106
39.
N. A. Sidorov, M. V. Falaleev, “In the memory of Trenogin Vladilen Aleksandrovich”, IIGU Ser. Matematika, 6:4 (2013), 138–140
2012
40.
N. A. Sidorov, R. Yu. Leontiev, A. I. Dreglea, “On Small Solutions of Nonlinear Equations with Vector Parameter in Sectorial Neighborhoods”, Math. Notes, 91:1 (2012), 90–104
41.
N. A. Sidorov, D. N. Sidorov, R. Yu. Leont'ev, “Successive approximations to solutions of nonlinear equations with vector parameter in the irregular case”, J. Appl. Industr. Math., 6:3 (2012), 387–392
42.
Denis N. Sidorov, Nikolai A. Sidorov, “Convex majorants method in the theory of nonlinear Volterra equations”, Banach J. Math. Anal., 6:1 (2012), 1–10
43.
N. A. Sidorov, D. N. Sidorov, “On successive approximations of solutions of a singular Cauchy problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 238–244
44.
N. A. Sidorov, M. V. Falaleev, “Continuous and generalized solutions of singular integro-differential equations in Banach spaces”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 11, 62–74
2011
45.
N. A. Sidorov, D. N. Sidorov, “Small solutions of nonlinear differential equations near branching points”, Russian Math. (Iz. VUZ), 55:5 (2011), 43–50
46.
D. N. Sidorov, N. A. Sidorov, “Generalized solutions in the problem of dynamical systems modeling by Volterra polynomials”, Autom. Remote Control, 72:6 (2011), 1258–1263
47.
R. Y. Leontyev, N. A. Sidorov, “An uniformization and successive approximation of solutions of nonlinear equations with vector parameter”, IIGU Ser. Matematika, 4:3 (2011), 116–123
48.
D. N. Sidorov, N. A. Sidorov, “Method of monotone majorants of the theory of nonlinear Volterra equations”, IIGU Ser. Matematika, 4:1 (2011), 97–108
49.
N. A. Sidorov, M. V. Falaleev, O. A. Romanova, “Vladilen Aleksandrovich Trenogin”, IIGU Ser. Matematika, 4:3 (2011), 171–172
2010
50.
N. A. Sidorov, D. N. Sidorov, A. V. Krasnik, “On the solution of Volterra operator-integral equations in an irregular case by the method of successive approximations”, Differ. Uravn., 46:6 (2010), 874–882
51.
N. A. Sidorov, D. N. Sidorov, “Solving the Hammerstein integral equation in the irregular case by successive approximations”, Siberian Math. J., 51:2 (2010), 325–329
52.
N. A. Sidorov, A. V. Trufanov, “Nonlinear operator equations with functionaly modified argument”, IIGU Ser. Matematika, 3:4 (2010), 96–113
53.
N. A. Sidorov, D. N. Sidorov, “Branching solutions of nonlinear differential equations of $n$-th order”, IIGU Ser. Matematika, 3:1 (2010), 92–103
54.
N. A. Sidorov, R. Yu. Leont'ev, “On solutions with the maximal order of vanishing of nonlinear equations with a vector parameter in sectorial neighborhoods”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 2, 2010, 226–237
2009
55.
N. A. Sidorov, A. V. Trufanov, “Nonlinear operator equations with functional perturbation of an argument of neutral type”, Differ. Uravn., 45:12 (2009), 1804–1808
56.
N. A. Sidorov, D. N. Sidorov, “Generalized solutions to integral equations in the problem of identification of nonlinear dynamic models”, Autom. Remote Control, 70:4 (2009), 598–604
2006
57.
N. A. Sidorov, A. V. Trufanov, D. N. Sidorov, “Generalized solutions of nonlinear integral-functional equations”, Nelineĭn. Granichnye Zadachi, 16 (2006), 96–106
58.
N. A. Sidorov, D. N. Sidorov, “Existence and construction of generalized solutions of nonlinear Volterra integral equations of the first kind”, Differ. Equ., 42:9 (2006), 1312–1316
59.
Nikolai A. Sidorov, Michail V. Falaleev, Denis N. Sidorov, “Generalized solutions of Volterra integral equations of the first kind”, Bull. Malays. Math. Sci. Soc. (2), 29:2 (2006), 101–109
2005
60.
M. V. Falaleev, N. A. Sidorov, D. N. Sidorov, “Generalized solutions of Volterra integral equations of the first kind”, Lobachevskii J. Math., 20 (2005), 47–57
61.
M. V. Falaleev, N. A. Sidorov, “Continuous and generalized solutions of singular partial differential equations”, Lobachevskii J. Math., 20 (2005), 31–45
N. A. Sidorov, A. V. Sinitsyn, “The stationary Vlasov-Maxwell system in bounded domains”, Nonlinear analysis and nonlinear differential equations (Russian), FizMatLit, Moscow, 2003, 50–88
63.
N. A. Sidorov, V. A. Trenogin, “Bifurcation points of solutions of nonlinear equations”, Nonlinear analysis and nonlinear differential equations (Russian), FizMatLit, Moscow, 2003, 5–49
64.
Michael V. Falaleev, Olga A. Romanova, Nicholas A. Sidorov, “Generalized Jordan sets in the theory of singular partial differential-operator equations”, Computational Science—{Iccs} 2003. Part II, Lecture Notes in Comput. Sci., 2658, Springer, Berlin, 2003, 523–532
2002
65.
N. Sidorov, B. Loginov, A. Sinitsyn, M. Falaleev, Lyapunov-Schmidt methods in nonlinear analysis and applications, Mathematics and its Applications, 550, Kluwer Academic Publishers, Dordrecht, 2002
66.
N. A. Sidorov, V. R. Abdullin, “Intertwined branching equations in the theory of nonlinear equations”, Sobolev-type equations (Russian), Chelyab. Gos. Univ., Chelyabinsk, 2002, 83–115
2001
67.
N. A. Sidorov, “Parametrization of simple branching solutions of full rank and iterations in nonlinear analysis”, Russian Math. (Iz. VUZ), 45:9 (2001), 55–61
68.
N. A. Sidorov, V. R. Abdullin, “Interlaced branching equations in the theory of non-linear equations”, Sb. Math., 192:7 (2001), 1035–1052
69.
V. R. Abdullin, N. A. Sidorov, “Interlaced equations in branching theory”, Dokl. Akad. Nauk, 377:3 (2001), 295–297
2000
70.
B. V. Loginov, D. G. Rakhimov, N. A. Sidorov, “Development of M. K. Gavurin's pseudoperturbation method”, Operator theory and its applications (Winnipeg, MB, 1998), Fields Inst. Commun., 25, Amer. Math. Soc., Providence, RI, 2000, 367–381
1999
71.
N. A. Sidorov, V. R. Abdullin, “Interlaced branching equations and invariance in the theory of nonlinear equations”, Symmetry and perturbation theory (Rome, 1998), World Sci. Publ., River Edge, NJ, 1999, 309–313
72.
N. A. Sidorov, “The initial-value problem for differential equations with a Fredholm operator in the principal part”, Vestnik Chelyabinsk. Univ. Ser. 3 Mat. Mekh., 1999, no. 2(5), 103–112
73.
N. A. Sidorov, A. V. Sinitsyn, “Index theory in the bifurcation problem of solutions of the Vlasov–Maxwell system”, Matem. Mod., 11:9 (1999), 83–100
74.
N. A. Sidorov, A. V. Sinitsyn, “On bifurcation points of the stationary Vlasov-Maxwell system with bifurcation direction”, Progress in Industrial Mathematics At {Ecmi} 98 (Gothenburg), European Consort. Math. Indust., Teubner, Stuttgart, 1999, 295–302
75.
N. A. Sidorov, Vestnik Chelyabinsk. Gos. Univ., 1999, no. 5, 103–112
1997
76.
N. A. Sidorov, “Implicit parametrization of solutions of the bifurcation equation”, Boundary value problems (Russian), Irkutsk. Gos. Univ., Irkutsk, 1997, 176–186, 207
77.
N. A. Sidorov, A. V. Sinitsyn, “Analysis of bifurcation points and nontrivial branches of solutions to the stationary Vlasov–Maxwell system”, Math. Notes, 62:2 (1997), 223–243
78.
N. A. Sidorov, “An $N$-step iterative method in the theory of the branching of solutions of nonlinear equations”, Siberian Math. J., 38:2 (1997), 330–341
79.
B. V. Loginov, N. A. Sidorov, Yu. B. Rusak, Matem. Mod., 9:10 (1997), 30–31
1996
80.
N. A. Sidorov, A. V. Sinitsyn, “Nontrivial solutions and bifurcation points of the Vlasov-Maxwell system”, Dokl. Akad. Nauk, 349:1 (1996), 26–28
N. A. Sidorov, A. V. Sinitsyn, “On the branching of solutions of the Vlasov–Maxwell system”, Siberian Math. J., 37:6 (1996), 1199–1211
1995
82.
N. A. Sidorov, “Explicit and implicit parametrizations in the construction of branching solutions by iterative methods”, Sb. Math., 186:2 (1995), 297–310
1994
83.
N. A. Sidorov, “Explicit parametrization of the solutions of nonlinear equations in a neighborhood of a branching point”, Dokl. Math., 49:3 (1994), 568–571
84.
N. A. Sidorov, O. A. Romanova, E. B. Blagodatskaya, “Partial differential equations with an operator of finite index at the principal part”, Differ. Equ., 30:4 (1994), 676–678
1992
85.
N. A. Sidorov, O. A. Romanova, E. B. Blagodatskaya, “Differential equations with an operator of finite index in the main part”, Approximate methods for solving operator equations (Russian), Irkutsk. Gos. Ped. Inst., Irkutsk, 1992, 75–79
86.
N. A. Sidorov, D. A. Tolstonogov, “Asymptotics and iterations in a neighborhood of the branching points of the solution of nonlinear equations”, Numerical methods in optimization and analysis (Russian) (Irkutsk, 1989), “Nauka” Sibirsk. Otdel., Novosibirsk, 1992, 162–171
87.
V. A. Trenogin, N. A. Sidorov, “Potentiality conditions for a branching equation and bifurcation points of nonlinear operators”, Uzbek. Mat. Zh., 1992, no. 2, 40–49
88.
Y. Markov, G. Rudykh, N. Sidorov, A. Sinitsyn, D. Tolstonogov, “Steady-state solutions of the Vlasov-Maxwell system and their stability”, Acta Appl. Math., 28:3 (1992), 253–293
89.
N. A. Sidorov, E. B. Blagodatskaya, “Differential equations with a Fredholm operator in the main differential expression”, Dokl. Math., 44:1 (1992), 302–305
90.
B. V. Loginov, N. A. Sidorov, “Group symmetry of the Lyapunov–Schmidt branching equation and iterative methods in the problem of a bifurcation point”, Math. USSR-Sb., 73:1 (1992), 67–77
1990
91.
Yu. A. Markov, G. A. Rudykh, N. A. Sidorov, A. V. Sinitzin, “Some families of solutions of the Vlasov-Maxwell system and their stability”, The Lyapunov functions method and applications, Imacs Ann. Comput. Appl. Math., 8, Baltzer, Basel, 1990, 197–203
92.
Yu. A. Markov, G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Some families of solutions of the Vlasov–Maxwell system and their stability”, Matem. Mod., 2:12 (1990), 88–101
93.
V. A. Trenogin, N. A. Sidorov, B. V. Loginov, “Potentiality, group symmetry and bifurcation in the theory of branching equation”, Differential Integral Equations, 3:1 (1990), 145–154
94.
V. A. Trenogin, N. A. Sidorov, B. V. Loginov, “The bifurcation equation: potentiality, bifurcation, symmetry”, Dokl. Math., 40:3 (1990), 517–520
1989
95.
Yu. A. Markov, G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Existence of stationary solutions of Vlasov–Maxwell equations and some of their exact solutions”, Matem. Mod., 1:6 (1989), 95–107
96.
G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Nonstationary solutions of the two-particle Vlasov–Maxwell system”, Dokl. Math., 34:8 (1989), 700–701
97.
G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Bifurcating stationary solutions of a two-particle Vlasov-Maxwell system”, Dokl. Math., 34:2 (1989), 122–123
1988
98.
G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Some exact solutions of a stationary system of Vlasov-Maxwell equations”, Problems in the qualitative theory of differential equations (Russian) (Irkutsk, 1986), “Nauka” Sibirsk. Otdel., Novosibirsk, 1988, 118–128, 283
99.
G. A. Rudykh, N. A. Sidorov, A. V. Sinitsyn, “Stationary solutions of a system of Vlasov–Maxwell equations”, Dokl. Math., 33:9 (1988), 673–674
1987
100.
N. A. Sidorov, M. V. Falaleev, “Generalized solutions of degenerate differential and integral equations in Banach spaces”, The method of Lyapunov functions in the analysis of the dynamics of systems (Irkutsk, 1985) (Russian), “Nauka” Sibirsk. Otdel., Novosibirsk, 1987, 308–318, 328
101.
V. A. Trenogin, B. V. Doginov, N. A. Sidorov, Proceedings of the Eleventh International Conference on Nonlinear Oscillations (Budapest, 1987), János Bolyai Math. Soc., Budapest, 1987, 502–505
102.
N. A. Sidorov, M. V. Falaleev, “Generalized solution of differential equations with a Fredholm operator at the derivative”, Differ. Uravn., 23:4 (1987), 726–728
1985
103.
B. V. Loginov, N. A. Sidorov, “A general method for the construction of the Lyapunov-Schmidt bifurcation equation, and some methods for its investigation”, Nonclassical problems of mathematical physics (Russian), “Fan”, Tashkent, 1985, 113–145, 232
1984
104.
N. A. Sidorov, “Lyapunov's methods in the theory of differential equations with a Volterra operator multiplying the derivative”, The method of Lyapunov functions and its applications, “Nauka” Sibirsk. Otdel., Novosibirsk, 1984, 241–251
105.
N. A. Sidorov, “A class of degenerate differential equations with convergence”, Math. Notes, 35:4 (1984), 300–305
106.
N. A. Sidorov, “Differential equations with a Volterra operator multiplying the derivative”, Soviet Math. (Iz. VUZ), 28:1 (1984), 95–104
1983
107.
B. V. Loginov, N. A. Sidorov, “Methods for the construction and use of the Lyapunov-Schmidt branching equation in the non-Fredholm case”, Theory and methods for solving ill-posed problems and their applications (Samarkand, 1983), Novosibirsk. Gos. Univ., Novosibirsk, 1983, 256–259
108.
N. A. Sidorov, O. A. Romanova, “Application of certain results of branching theory in the solution of degenerate differential equations”, Differ. Uravn., 19:9 (1983), 1516–1526
1982
109.
N. A. Sidorov, Obshchie voprosy regulyarizatsii v zadachakh teorii vetvleniya, Irkutsk. Gos. Univ., Irkutsk, 1982
110.
N. A. Sidorov, “Solution of integro-differential equations with noninvertible operator multiplying the derivative”, Approximate methods for solving operator equations and their applications, Akad. Nauk Sssr Sibirsk. Otdel., Ènerget. Inst., Irkutsk, 1982, 121–130
111.
O. A. Romanova, N. A. Sidorov, “The role of Schmidt's lemma and pseudoinverse operators in the theory of differential equations with degeneration”, Analytic methods in the theory of elliptic equations, “Nauka” Sibirsk. Otdel., Novosibirsk, 1982, 82–88
1981
112.
N. A. Sidorov, O. A. Romanova, “Theorems on the existence of solutions for differential equations with degeneration and discontinuous right-hand side”, Discrete and distributed systems, Irkutsk. Gos. Univ., Irkutsk, 1981, 78–89, 223
113.
N. A. Sidorov, “Branching of solutions of nonlinear equations with a potential branching equation”, Dokl. Akad. Nauk Sssr, 256:6 (1981), 1322–1326
1980
114.
N. A. Sidorov, V. A. Trenogin, “Regularization of linear controls on the basis of perturbation theory”, Differ. Uravn., 16:11 (1980), 2039–2049
1979
115.
N. A. Sidorov, “Regularization of an inverse boundary value problem”, Application of the methods of functional analysis to problems of mathematical physics and numerical analysis (Russian), Akad. Nauk Sssr Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1979, 123–128
1978
116.
N. A. Sidorov, “The calculation of eigenvalues and -vectors of linear operators on the basis of the theory of perturbations”, Differ. Uravn., 14:8 (1978), 1522–1525
117.
V. A. Trenogin, N. A. Sidorov, “Regularization of simple solutions of nonlinear equations in the neighborhood of a bifurcation point”, Siberian Math. J., 19:1 (1978), 128–132
118.
N. A. Sidorov, “Regularization of linear differential equations with constant operators in the degenerate case”, Differ. Uravn., 14:3 (1978), 556–560
1977
119.
N. A. Sidorov, “Integral systems of branching of degenerate differential equations”, Questions in applied mathematics (Russian), Sibirsk. Ènerget. Inst., Akad. Nauk Sssr Sibirsk. Otdel., Irkutsk, 1977, 177–179
120.
N. A. Sidorov, “The method of continuation with respect to the parameter in the neighborhood of a branch point”, Questions in applied mathematics (Russian), Sibirsk. Ènerget. Inst., Akad. Nauk Sssr Sibirsk. Otdel., Irkutsk, 1977, 109–113
121.
N. A. Sidorov, “Two-step regularization of the computation of the solutions of nonlinear equations in the neighborhood of a bifurcation point”, Partial differential equations and their applications (Russian), Izdat. “Fan” Uzbek. SSR, Tashkent, 1977, 120–129, 183
122.
B. V. Loginov, N. A. Sidorov, “Calculation of the eigenvalues and eigenelements of linear operators by the method of false perturbations”, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, 1977, no. 5, 26–29, 102
123.
V. A. Trenogin, N. A. Sidorov, “Regularisation of computation of branching solutions of nonlinear equations”, Singular perturbations and boundary layer theory (Proc. Conf., École Centrale, Lyon, 1976), Springer, Berlin, 1977, 491–505. Lecture Notes in Math., Vol. 594
N. A. Sidorov, “A study of the continuous solutions of the Cauchy problem in the neighborhood of a branch point”, Soviet Math. (Iz. VUZ), 20:9 (1976), 77–87
125.
B. V. Loginov, N. A. Sidorov, “Calculation of eigenvalues and eigenvectors of bounded operators by the false-perturbation method”, Math. Notes, 19:1 (1976), 62–64
126.
N. A. Sidorov, V. A. Trenogin, “A certain approach to the problem of regularization on the basis of the perturbation of linear operators”, Math. Notes, 20:5 (1976), 976–979
127.
N. A. Sidorov, “The optimal choice of initial approximations to solutions of regularized equations in the theory of branching”, Math. Notes, 20:2 (1976), 710–713
128.
V. A. Trenogin, N. A. Sidorov, “Tihonov regularization of the problem of bifurcation points of nonlinear operators”, Siberian Math. J., 17:2 (1976), 314–323
129.
N. A. Sidorov, V. A. Trenogin, “Regularization of the computation of the real solutions of nonlinear equations in the neighborhood of a branch point”, Dokl. Akad. Nauk Sssr, 228:5 (1976), 1049–1052
1975
130.
N. A. Sidorov, V. A. Trenogin, “Regularization in the sense of A. N. Tihonov of some problems in bifurcation theory”, Differential and integral equations, No. 3 (Russian), Irkutsk. Gos. Univ., Irkutsk, 1975, 183–193, 302
131.
N. A. Sidorov, “Investigation of linear differential equations with constant operators in the degenerate case”, Differential and integral equations, No. 3 (Russian), Irkutsk. Gos. Univ., Irkutsk, 1975, 178–182, 302
1973
132.
N. A. Sidorov, “Variational methods in the theory of the bifurcation points of nonlinear operators”, Differential and integral equations, No. 2 (Russian), Irkutsk. Gos. Univ., Irkutsk, 1973, 255–270, 315–316
133.
N. A. Sidorov, “The branching of the solutions of differential equations with a degeneracy”, Differ. Uravn., 9:8 (1973), 1464–1481
1972
134.
V. A. Trenogin, N. A. Sidorov, “An investigation of the bifurcation points and nontrivial branches of the solutions of nonlinear equations”, Differential and integral equations, No. 1 (Russian), Irkutsk. Gos. Univ., Irkutsk, 1972, 216–247
135.
N. A. Sidorov, “The Cauchy problem for a certain class of differential equations”, Differ. Uravn., 8:8 (1972), 1521–1524
1969
136.
N. A. Sidorov, L. V. Zorik, “The investigation of a certain integral equation with deviating argument”, Trudy Irkutsk. Gos. Univ., 64 (1969), 36–41
1968
137.
N. A. Sidorov, “The singular solutions of a certain class of integro-partial differential equations”, Trudy Irkutsk. Gos. Univ., 26 (1968), 36–45
138.
N. A. Sidorov, “The branch points and singular solutions of certain classes of integral and integro-differential equations with two parameters”, Trudy Irkutsk. Gos. Univ., 26 (1968), 66–73
139.
N. A. Sidorov, “Solution of the Cauchy problem for a certain class of integro-differential equations with analytic nonlinearities”, Differ. Uravn., 4:7 (1968), 1309–1316
1967
140.
N. A. Sidorov, “A solution of a certain class of nonlinear integro-partial differential equations”, Proc. Sixth Interuniv. Sci. Conf. of the Far East on Physics and Mathematics, Vol. 3: Differential and Integral Equations (Russian), Habarovsk. Gos. Ped. Inst., Khabarovsk, 1967, 174–179
141.
N. A. Sidorov, “The branching of the solutions of certain classes of integro-differential equations”, Proc. Sixth Interuniv. Sci. Conf. of the Far East on Physics and Mathematics, Vol. 3: Differential and Integral Equations (Russian), Habarovsk. Gos. Ped. Inst., Khabarovsk, 1967, 167–173
142.
N. A. Sidorov, “Branching of solutions of the Cauchy problem for a class of nonlinear integro-differential equations”, Differ. Uravn., 3:9 (1967), 1592–1601
1966
143.
N. A. Sidorov, “Application of a Newton diagram to the determination of singular solutions of integro-differential equations”, Communications of Works of the Irkutsk State Univ. Comput. Center, No. I (Russian), Irkutsk. Gos. Univ. Vyčisl. Centr, Irkutsk, 1966, 276–277
144.
N. A. Sidorov, “The singular solutions of certain classes of integro-differential equations”, Communications of Works of the Irkutsk State Univ. Comput. Center, No. I (Russian), Irkutsk. Gos. Univ. Vyčisl. Centr, Irkutsk, 1966, 72–77
145.
N. A. Sidorov, “The branching of the solutions of the Cauchy problem for a certain class of nonlinear integro-differential equations”, Communications of Works of the Irkutsk State Univ. Comput. Center, No. I (Russian), Irkutsk. Gos. Univ. Vyčisl. Centr, Irkutsk, 1966, 27–46
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