A. V. Arutyunov, S. E. Zhukovskiy, Mat. Sb., 215:9 (2024) (to appear)
2.
A. V. Arutyunov, S. E. Zhukovskiy, “On the Second Order Sufficient Optimality Conditions for a Problem of Mathematical Programming”, Math. Notes, 115:2 (2024), 148–164
3.
A. V. Arutyunov, S. E. Zhukovskiy, “Applications of $\lambda$-truncations to the study of local and global solvability of nonlinear equations”, Eurasian Math. J., 15:1 (2024), 23–33;
4.
A. V. Arutyunov, S. E. Zhukovskiy, K. A. Tsarkov, “Stability of solutions to extremal problems with constraints based on $\lambda$-truncations”, Avtomat. i Telemekh., 2024, no. 2, 3–20
2023
5.
A. V. Arutyunov, S. E. Zhukovskiy, B. Sh. Mordukhovich, “Implicit Function Theorems for Continuous Mappings
and Their Applications”, Math. Notes, 113:6 (2023), 749–759
6.
A. V. Arutyunov, S. E. Zhukovskiy, “On the Lagrange multiplier rule for minimizing sequences”, Eurasian Math. J., 14:1 (2023), 8–15;
A. V. Arutyunov, S. E. Zhukovskiy, “Stability of Real Solutions to Nonlinear Equations and Its Applications”, Proc. Steklov Inst. Math., 323 (2023), 1–11
8.
A. V. Arutyunov, S. E. Zhukovskiy, “Generalization of Banach’s theorem for cones and covering along curves”, Russian Universities Reports. Mathematics, 28:144 (2023), 361–370
2022
9.
A. V. Arutyunov, A. V. Greshnov, “$(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points. A review of the results”, Fixed Point Theory, 23:2 (2022), 473–486
A. V. Arutyunov, S. E. Zhukovskiy, “Global and semilocal theorems on implicit and inverse functions in Banach spaces”, Sb. Math., 213:1 (2022), 1–41
11.
A. V. Arutyunov, Z. T. Zhukovskaya, S. E. Zhukovskiy, “Antiperiodic boundary value problem for an implicit ordinary differential equation”, Russian Universities Reports. Mathematics, 27:139 (2022), 205–213
2021
12.
A. V. Arutyunov, S. E. Zhukovskiy, “On global solvability of nonlinear equations with parameters”, Dokl. Math., 103:1 (2021), 57–60
13.
A. V. Arutyunov, S. E. Zhukovskiy, “On exact penalties for constrained optimization problems in metric spaces”, Eurasian Math. J., 12:4 (2021), 10–20;
A. V. Arutyunov, “Existence of Real Solutions of Nonlinear Equations without A Priori Normality Assumptions”, Math. Notes, 109:1 (2021), 3–14
15.
A. V. Arutyunov, K. I. Salikhova, “Implicit Function Theorem in a Neighborhood of an Abnormal Point”, Proc. Steklov Inst. Math., 315 (2021), 19–26
16.
A. V. Arutyunov, S. E. Zhukovskiy, “Covering Mappings Acting into Normed Spaces and Coincidence Points”, Proc. Steklov Inst. Math., 315 (2021), 13–18
17.
A. V. Arutyunov, S. E. Zhukovskiy, “Stable Solvability of Nonlinear Equations under Completely Continuous Perturbations”, Proc. Steklov Inst. Math., 312 (2021), 1–15
18.
A. V. Arutyunov, E. A. Pluzhnikova, “On the Cauchy problem for implicit differential equations of higher orders”, Russian Universities Reports. Mathematics, 26:136 (2021), 348–362
2020
19.
A. V. Arutyunov, S. E. Zhukovskiy, “On stability of continuous extensions of mappings with respect to Nemytskii operator”, Dokl. Math., 101:3 (2020), 182–184
20.
A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Coincidence Points and Generalized Coincidence Points of Two Set-Valued Mappings”, Proc. Steklov Inst. Math., 308 (2020), 35–41
2019
21.
A. V. Arutyunov, “IInvestigation of the sets of real solutions of non-linear equations”, Izv. Math., 83:2 (2019), 199–213
22.
A. V. Arutyunov, S. E. Zhukovskiy, “Hadamard's theorem for mappings with relaxed smoothness conditions”, Sb. Math., 210:2 (2019), 165–183
23.
A. V. Arutyunov, S. E. Zhukovskiy, K. V. Storozhuk, “The structure of the set of local minima of functions in various spaces”, Siberian Math. J., 60:3 (2019), 398–404
24.
A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Kantorovich's Fixed Point Theorem in Metric Spaces and Coincidence Points”, Proc. Steklov Inst. Math., 304 (2019), 60–73
2018
25.
A. V. Arutyunov, A. V. Greshnov, “$(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points”, Izv. Math., 82:2 (2018), 245–272
26.
A. V. Arutyunov, S. E. Zhukovskii, “Variational Principles in Nonlinear Analysis and Their Generalization”, Math. Notes, 103:6 (2018), 1014–1019
27.
A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “On the cardinality of the coincidence set for mappings of metric, normed and partially ordered spaces”, Sb. Math., 209:8 (2018), 1107–1130
28.
A. V. Arutyunov, K. Yu. Osipenko, “Recovering linear operators and Lagrange function minimality condition”, Siberian Math. J., 59:1 (2018), 11–21
2017
29.
A.V. Arutyunov, A.V. Greshnov, L.V. Lokoutsievskii, K.V. Storozhuk, “Topological and geometrical properties of spaces with symmetric and nonsymmetric $f$-quasimetrics”, Topology Appl., 221 (2017), 178–194;
A. V. Arutyunov, S. E. Zhukovskiy, D. Yu. Karamzin, “Some properties of two-dimensional surjective $p$-homogeneous maps”, Comput. Math. Math. Phys., 57:7 (2017), 1081–1089
2016
31.
A. V. Arutyunov, N. G. Pavlova, A. A. Shananin, “Equilibrium prices in an economic equilibrium model”, Matem. Mod., 28:3 (2016), 3–22
32.
A. V. Arutyunov, S. E. Zhukovskii, “On Surjective Quadratic Mappings”, Math. Notes, 99:2 (2016), 192–195
33.
A. V. Arutyunov, S. E. Zhukovskiy, “Properties of surjective real quadratic maps”, Sb. Math., 207:9 (2016), 1187–1214
2015
34.
A. V. Arutyunov, B. D. Gel'man, “On the structure of the set of coincidence points”, Sb. Math., 206:3 (2015), 370–388
35.
A. V. Arutyunov, “Caristi's condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points”, Proc. Steklov Inst. Math., 291 (2015), 24–37
36.
A. V. Arutyunov, S. E. Zhukovskiy, “On estimates for solutions of systems of convex inequalities”, Comput. Math. Math. Phys., 55:9 (2015), 1444–1450
2014
37.
A. V. Arutyunov, “Coincidence Points of Two Maps”, Funct. Anal. Appl., 48:1 (2014), 72–75
2016
38.
A. V. Arutyunov, S. E. Zhukovskiy, “On the continuity of inverse mappings for Lipschitz perturbations of covering mappings”, J. Math. Sci., 217:6 (2016), 731–735
2014
39.
E. R. Avakov, A. V. Arutyunov, D. Yu. Karamzin, “An investigation of smooth maps in a neighbourhood of an abnormal point”, Izv. Math., 78:2 (2014), 213–250
2016
40.
A. V. Arutyunov, D. Yu. Karamzin, F. L. Pereira, “Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 27–35
2013
41.
A. V. Arutyunov, “Properties of the Minimum Function in the Quadratic Problem”, Math. Notes, 94:1 (2013), 32–40
42.
A. V. Arutyunov, S. E. Zhukovskiy, N. G. Pavlova, “Equilibrium price as a coincidence point of two mappings”, Comput. Math. Math. Phys., 53:2 (2013), 158–169
2012
43.
A. V. Arutyunov, “Two Problems of the Theory of Quadratic Maps”, Funct. Anal. Appl., 46:3 (2012), 225–227
44.
A. V. Arutyunov, “Smooth abnormal problems in extremum theory and analysis”, Russian Math. Surveys, 67:3 (2012), 403–457
45.
A. V. Arutyunov, “An iterative method for finding coincidence points of two mappings”, Comput. Math. Math. Phys., 52:11 (2012), 1483–1486
46.
A. V. Arutyunov, S. E. Zhukovskiy, Z. T. Mingaleeva, “Differential properties of the minimum function for diagonalizable quadratic problems”, Comput. Math. Math. Phys., 52:10 (2012), 1342–1350
2011
47.
A. V. Arutyunov, D. Yu. Karamzin, “Regular zeros of quadratic maps and their application”, Sb. Math., 202:6 (2011), 783–806
2010
48.
A. V. Arutyunov, “On implicit function theorems at abnormal points”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S18–S27
49.
A. V. Arutyunov, S. E. Zhukovskiy, “Existence and properties of inverse mappings”, Proc. Steklov Inst. Math., 271 (2010), 12–22
50.
A. V. Arutyunov, D. A. Zhukov, “Investigation of a linear optimal control problem with state constraints”, Vladikavkaz. Mat. Zh., 12:1 (2010), 3–9
2009
51.
A. V. Arutyunov, “Stability of Coincidence Points and Properties of Covering Mappings”, Math. Notes, 86:2 (2009), 153–158
52.
A. V. Arutyunov, B. D. Gel'man, “Minimum of a functional in a metric space and fixed points”, Comput. Math. Math. Phys., 49:7 (2009), 1111–1118
2008
53.
A. V. Arutyunov, “Nonnegativity of Quadratic Forms on Intersections of Quadrics and Quadratic Maps”, Math. Notes, 84:2 (2008), 155–165
54.
E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “Exact penalties for optimization problems with 2-regular equality constraints”, Comput. Math. Math. Phys., 48:3 (2008), 346–353
2007
55.
E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “Necessary Conditions for an Extremum in a Mathematical Programming Problem”, Proc. Steklov Inst. Math., 256 (2007), 2–25
56.
A. V. Arutyunov, D. Yu. Karamzin, “Necessary optimality conditions for abnormal problems with geometric constraints”, Comput. Math. Math. Phys., 47:3 (2007), 349–360
2006
57.
A. V. Arutyunov, “Controllability of nonlinear systems with constrained controls”, Differ. Equ., 42:11 (2006), 1515–1523
58.
A. V. Arutyunov, D. Yu. Karamzin, “Necessary optimality conditions in an abnormal optimization problem with equality constraints”, Comput. Math. Math. Phys., 46:8 (2006), 1293–1298
59.
A. V. Arutyunov, E. V. Kruglova, “On the consistency of linear and quadratic systems”, Comput. Math. Math. Phys., 46:4 (2006), 537–540
60.
A. V. Arutyunov, “An implicit function theorem without a priori assumptions about normality”, Comput. Math. Math. Phys., 46:2 (2006), 195–205
2005
61.
A. V. Arutyunov, D. Yu. Karamzin, “Necessary Conditions for a Weak Minimum in an Optimal Control Problem with Mixed Constraints”, Differ. Equ., 41:11 (2005), 1532–1543
62.
A. V. Arutyunov, “Implicit-Function Theorem on the Cone in a Neighborhood of an Irregular Point”, Math. Notes, 78:4 (2005), 573–576
63.
A. V. Arutyunov, “Covering of nonlinear maps on a cone in neighborhoods of irregular points”, Math. Notes, 77:4 (2005), 447–460
64.
A. V. Arutyunov, “On real quadratic forms annihilating an intersection of quadrics”, Russian Math. Surveys, 60:1 (2005), 157–158
65.
E. R. Avakov, A. V. Arutyunov, “Inverse function theorem and conditions of extremum for abnormal problems with non-closed range”, Sb. Math., 196:9 (2005), 1251–1269
66.
A. V. Arutyunov, “Solvability conditions for nonlinear equations on a cone in a neighborhood of an anormal point”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 1, S25–S30
2004
67.
A. V. Arutyunov, N. G. Pavlova, “Topological properties of attainability sets of linear systems”, Differ. Equ., 40:11 (2004), 1645–1648
68.
A. V. Arutyunov, “Some elementary formulas of convex analysis”, Vladikavkaz. Mat. Zh., 6:4 (2004), 7–9
69.
E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “On convergence rate estimates for power penalty methods”, Comput. Math. Math. Phys., 44:10 (2004), 1684–1695
70.
A. V. Arutyunov, A. F. Izmailov, “Sensitivity analysis for abnormal optimization problems with a cone constraint”, Comput. Math. Math. Phys., 44:4 (2004), 552–574
2003
71.
A. V. Arutyunov, “The Pontryagin Maximum Principle and Sufficient Optimality Conditions for Nonlinear Problems”, Differ. Equ., 39:12 (2003), 1671–1679
72.
A. V. Arutyunov, R. B. Vinter, “A Finite-Dimensional Approximation Method in Optimal Control Theory”, Differ. Equ., 39:11 (2003), 1519–1528
73.
A. V. Arutyunov, A. F. Izmailov, “The sensitivity theory for abnormal optimization problems with equality constraints”, Comput. Math. Math. Phys., 43:2 (2003), 178–193
2002
74.
A. V. Arutyunov, V. N. Burkov, A. Yu. Zalozhnev, D. Yu. Karamzin, “A Problem of Optimal Distribution of Resources over a Set of Independent Operations”, Autom. Remote Control, 63:5 (2002), 792–802
75.
A. V. Arutyunov, Yu. S. Vereshchagina, “On Necessary Second-Order Conditions in Optimal Control Problems”, Differ. Equ., 38:11 (2002), 1531–1540
76.
A. V. Arutyunov, V. Jacimovic, “2-Normal Processes in Controlled Dynamical Systems”, Differ. Equ., 38:8 (2002), 1081–1094
77.
A. V. Arutyunov, “Positive Quadratic Forms on Intersections of Quadrics”, Math. Notes, 71:1 (2002), 25–33
78.
A. V. Arutyunov, “Necessary Extremum Conditions and an Inverse Function Theorem without a priori Normality Assumptions”, Proc. Steklov Inst. Math., 236 (2002), 25–36
79.
A. V. Arutyunov, A. F. Izmailov, “Checking the sign-definiteness of forms”, Comput. Math. Math. Phys., 42:6 (2002), 767–780
2001
80.
A. V. Arutyunov, “Milyutin's Theorem in Linear-Quadratic Optimal Control Problems”, Differ. Equ., 37:11 (2001), 1627–1630
2000
81.
A. V. Arutyunov, “Implicit function theorem as a realization of the Lagrange principle. Abnormal points”, Sb. Math., 191:1 (2000), 1–24
1999
82.
A. V. Arutyunov, V. N. Rozova, “Regular zeros of a quadratic mapping and local controllability of nonlinear systems”, Differ. Equ., 35:6 (1999), 723–728
2001
83.
A. V. Arutyunov, N. Yu. Chernikova, “On the controllability of trajectories in optimal control problems with phase constraints”, J. Math. Sci. (N. Y.), 103:6 (2001), 664–669
1998
84.
A. V. Arutyunov, “Relaxation and perturbation of optimal control problem”, Proc. Steklov Inst. Math., 220 (1998), 23–30
1996
85.
A. V. Arutyunov, “On the theory of abnormal extremal problems with a finite-dimensional image”, Dokl. Akad. Nauk, 348:3 (1996), 295–298
86.
A. V. Arutyunov, “Second-order conditions in extremal problems with finite-dimensional range. 2-normal maps”, Izv. Math., 60:1 (1996), 39–65
1995
87.
A. V. Arutyunov, “Investigation of quadratic forms of calculus of variations with exponential degeneracy on a small time interval”, Proc. Steklov Inst. Math., 211 (1995), 35–54
1994
88.
A. V. Arutyunov, S. M. Aseev, “The maximum principle in optimal control problems with phase constraints. Nondegeneracy and stability”, Dokl. Math., 49:1 (1994), 38–42
1995
89.
A. V. Arutyunov, “On the theory of degenerate quadratic forms in the classical calculus of variations”, Izv. Math., 45:3 (1995), 433–476
1994
90.
A. V. Arutyunov, “Degenerate quadratic forms of the calculus of variations”, Dokl. Math., 48:3 (1994), 491–497
91.
A. V. Arutyunov, S. M. Aseev, V. I. Blagodatskikh, “First-order necessary conditions in the problem of optimal control of a differential inclusion with phase constraints”, Sb. Math., 79:1 (1994), 117–139
1993
92.
A. V. Arutyunov, “Sign-definiteness of quadratic forms of the calculus of variations with power degeneration”, Dokl. Math., 46:2 (1993), 337–342
1992
93.
A. V. Arutyunov, “Higher-order extremum conditions in abnormal minimization problems”, Siberian Math. J., 33:4 (1992), 557–565
1991
94.
A. V. Arutyunov, “Properties of quadratic maps in a Banach space”, Math. Notes, 50:4 (1991), 993–999
1992
95.
E. R. Avakov, A. A. Agrachev, A. V. Arutyunov, “The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping”, Sb. Math., 73:2 (1992), 455–466
1993
96.
A. V. Arutyunov, V. I. Blagodatskikh, “Maximum-principle for differential inclusions with space constraints”, Proc. Steklov Inst. Math., 200 (1993), 3–25
1991
97.
A. V. Arutyunov, “Higher-order conditions in abnormal extremal problems with equality-type constraints”, Dokl. Math., 42:3 (1991), 799–804
98.
A. V. Arutyunov, “On the theory of quadratic mappings in Banach spaces”, Dokl. Math., 42:2 (1991), 621–623
1990
99.
A. V. Arutyunov, “Necessary conditions for an extremum in an abnormal problem with equality constraints”, Russian Math. Surveys, 45:5 (1990), 223–224
1989
100.
A. V. Arutyunov, “On the theory of the maximum principle in optimal control problems with phase constraints”, Dokl. Math., 39:1 (1989), 1–4
101.
A. V. Arutyunov, M. D. Mardanov, “On the theory of the maximum principle in problems with delays”, Differ. Equ., 25:12 (1989), 1443–1452
1991
102.
A. V. Arutyunov, “Perturbations of extremal problems with constraints, and necessary conditions for optimality”, J. Math. Sci. (N. Y.), 54:6 (1991), 1342–1400
1986
103.
A. V. Arutyunov, M. D. Mardanov, “On the theory of optimal processes with delays”, Differ. Uravn., 22:8 (1986), 1291–1298
1985
104.
A. V. Arutyunov, “On necessary conditions for optimality in a problem with phase constraints”, Dokl. Akad. Nauk SSSR, 280:5 (1985), 1033–1037
1984
105.
A. V. Arutyunov, N. T. Tynyanskii, “On necessary conditions for a local minimum in optimal control theory”, Dokl. Akad. Nauk SSSR, 275:2 (1984), 268–272
106.
A. V. Arutyunov, N. T. Tynyanskii, “The fixed sign property of quadratic forms on a cone”, Russian Math. Surveys, 39:2 (1984), 139–140
1983
107.
A. V. Arutyunov, “The first condition in L. S. Pontryagin's article: “On the theory of differential games” [Uspekhi Mat. Nauk 21 (1966), no. 4(130), 219–274; MR0204187]”, Differ. Uravn., 19:6 (1983), 923–938
1982
108.
A. V. Arutyunov, “On a class of linear processes of time-optimality”, Differ. Uravn., 18:4 (1982), 555–560
1983
109.
N. T. Tynyanskii, A. V. Arutyunov, “On the system of Jacobi equations in a time-optimal problem”, Izv. Math., 21:2 (1983), 375–397
1981
110.
A. V. Arutyunov, N. T. Tynyanskii, “On second-order conditions in a time-optimal problem”, Dokl. Akad. Nauk SSSR, 261:3 (1981), 523–526
111.
A. V. Arutyunov, N. T. Tynyanskii, “First- and second-order conditions in the problem of optimal high-speed”, Russian Math. Surveys, 36:6 (1981), 167–168
1980
112.
A. V. Arutyunov, “Convex properties of the legendre transform”, Math. Notes, 28:2 (1980), 591–595
1972
113.
A. V. Arutyunov, S. N. Banchila, L. P. Filippov, TVT, 10:3 (1972), 547–550
114.
A. V. Arutyunov, S. N. Banchila, L. P. Filippov, TVT, 10:2 (1972), 425–428
115.
A. V. Arutyunov, S. N. Banchila, TVT, 10:1 (1972), 190–192
1971
116.
A. V. Arutyunov, S. N. Banchila, L. P. Filippov, “Properties of titanium at temperatures above $1000^{\circ}$ K”, High Temperature, 9:3 (1971), 487–489
1970
117.
A. V. Arutyunov, L. P. Filippov, “Thermal properties of rhenium at high temperatures”, High Temperature, 8:5 (1970), 1025–1027
О неравенствах среднего значения S. E. Zhukovskiy, A. V. Arutyunov, Z. T. Zhukovskaya Noncommutative geometry and topology February 22, 2024 16:45
4.
On nonlocal inverse function theorems and their applications A. V. Arutyunov, S. E. Zhukovskiy International Conference “Differential Equations and Optimal Control” dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko June 9, 2022 16:30
5.
Some inverse function theorems A. V. Arutyunov, S. E. Zhukovskiy Geometric Theory of Optimal Control April 20, 2022 16:45
Теорема Канторовича о неподвижной точке и теоремы о точках совпадения отображений в пространстве с векторной метрикой А. В. Арутюнов, Е. С. Жуковский, С. Е. Жуковский International Scientific Conference KOLMOGOROV READINGS – IX. General Control Problems and their Applications (GCP–2020), dedicated to the 70-th birth anniversary of Alexander Ivanovich Bulgakov and to the 90-th anniversary of the Institute of Mathematics, Physics and Information
Technologies of Derzhavin Tambov State University October 14, 2020 18:55
9.
Глобальные теоремы о неявной функции А. В. Арутюнов, С. Е. Жуковский International Scientific Conference KOLMOGOROV READINGS – IX. General Control Problems and their Applications (GCP–2020), dedicated to the 70-th birth anniversary of Alexander Ivanovich Bulgakov and to the 90-th anniversary of the Institute of Mathematics, Physics and Information
Technologies of Derzhavin Tambov State University October 12, 2020 13:05
Coincidence points theory in metric spaces A. V. Arutyunov International Conference "Mathematical Theory of Optimal Control"
dedicated to the 90th birthday of Academician R. V. Gamkrelidze June 2, 2017 12:35
Равномерные оценки расстояний до множества точек совпадения A. V. Arutyunov, S. E. Zhukovskii, E. R. Avakov Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics December 2, 2015 16:00
О разрешимости уравнений Вольтерра неявного вида (продолжение) A. V. Arutyunov, S. E. Zhukovskii, E. S. Zhukovskii Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics March 12, 2014 16:00
30.
О разрешимости уравнений Вольтерра неявного вида A. V. Arutyunov, S. E. Zhukovskii, E. S. Zhukovskii Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics March 5, 2014 16:00
Abnormal problems in extremum theory and analysis A. V. Arutyunov Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin September 25, 2013 15:20
2024
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