nonlinear elliptic boundary value problems,
bifurcations of solutions,
blow-up solutions,
nonlinear parabolic problems,
p-Laplacian,
Yamabe problem,
compactons, Rayleigh quotient, Collatz-Wielandt formula
UDC:
517.9, 517.95
Subject:
existence and uniqueness of solutions of nonlinear differential equations, spectral theory of linear and nonlinear operators, finding branches of solutions of nonlinear partial differential equations, development of variational methods for studying nonlinear equations, development variational methods for finding critical characteristics of nonlinear models, development of new approaches for finding bifurcations of solutions of nonlinear equations, development of new approaches for the numerical analysis of critical phenomena in nonlinear models , mathematical physics, construction of a generalized Collatz-Wielandt formula and a generalized Rayleigh quotient for nonlinear problems, development of the theory of optimal inverse spectral problems, development of variational methods for studying special classes of solutions, including solutions with compact supports and free boundaries, blow-up solutions, ground states
Biography
1976–1981: undergraduate course at the Lomonosov Moscow State University, Faculty of Mechanics and Mathematics,
1981–1985: PhD course at the Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Department of Differential Equations,
1997–1999: Research Fellow (Doctorant), Steklov Mathematical Institute, Moscow.
Main publications:
Ilyasov Y.Sh., “Bifurcation calculus by the extended functional method”, Funct. Anal. Appl., 41:1 (2007), 18–30
Ilyasov Y., “A duality principle corresponding to the parabolic equations”, Physica D, 237:5 (2008), 692–698
Ilyasov Y., “On nonlocal existence results for elliptic equations with convex-concave nonlinearities”, Nonlinear Analysis, 61:1-2 (2005), 211–236
Ilyasov Y., Runst T., “On nonlocal calculation for inhomogeneous indefinite Neumann boundary value problems”, Calculus Var. & Part. Diff. Eq., 22:1 (2005), 101–127
Ilyasov Y., “On positive solutions of indefinite elliptic equations”, C. R. Acad. Sci. Paris S\er. I Math., 333:6 (2001), 533–538
L. Cherfils, Ya. Il’yasov, “On the stationary solutions of generalized reaction diffusion equations with p&q-Laplacian”, Commun. Pure Appl. Anal, 4:1 (2005), 9–22
Ya. Sh. Il'yasov, “Non-local investigation of bifurcations of solutions of non-linear elliptic equations”, Izv. Math., 66:6 (2002), 1103–1130
4.
Y, Sh. Ilyasov, N. F. Valeev, “On nonlinear boundary value problem corresponding to N-dimensional inverse spectral problem”, Journal of Differential Equations, 266:8 (2019), 4533-4543 , arXiv: 1803.01495
J. I. Díaz, J. Hernández, Ya. Il’yasov, “On the existence of positive solutions and solutions with compact support for a spectral nonlinear elliptic problem with strong absorption”, Nonlinear Analysis: Theory, Methods & Applications, 119 (2015), 484–500 , Pergamon
J.I. Díaz, J. Hernández, and Y.S. Ilyasov, ,, “On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of star-shaped sets.”, Advances in Nonlinear Analysis, 9:1 (2020) , 19 pp. 10.1515/anona-2020-0030
J. I. Díaz, J. Hernández, Y. Sh. Ilyasov, “On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets”, Advances in Nonlinear Analysis, 9:1 (2019), 1046-1065 , arXiv: 1808.03931
Ya. Sh. Il'yasov, P. Taká{\v}, “Optimal $W\sp {2,2}\sb {\rm loc}$-regularity, ohozhaev's identity, and nonexistence of weak solutions to some quasilinear elliptic equations”, J. Differential Equations, 252:3 (2012), 2792–2822
Salazar, Pablo Daniel Paz, Yavdat Ilyasov, Luís Fernando Costa Alberto, Eduardo Coelho Marques Costa, and Mauricio BC Salles., “Saddle-Node Bifurcations of Power Systems in the Context of Variational Theory and Nonsmooth Optimization”, IEEE Access, 8 (2020) , 7 pp. 10.1109/ACCESS.2020.3002840
Yavdat Ilyasov, Nur Valeev, “Recovery of the nearest potential field from the m observed eigenvalues”, Physica D: Nonlinear Phenomena, 426 (2021) , 5 pp. 10.1016/j.physd.2021.132985
J. I. Díaz, J. Hernández, and Y. Ilyasov., “Stability criteria on flat and compactly supported ground states of some non-Lipschitz autonomous semilinear equations”, Chinese Ann. Math, 38 (2017) (to appear) , 33 pp. 10.1007/s11401-016-1073-2.
Jesus Ildefonso Diaz, Jesus Hernandez and Yavdat Il'yasov, “Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for $N\geq 3$”, Special Issue of Chinese Annals of Mathematics (CAM) in honour of Haim Brezis., 38B:4 (2016), 1–34
Ya. Il'yasov, Th. Runst, “Positive solutions of indefinite equations with p-Laplacian and supercritical nonlinearity”, Complex Variables and Elliptic Equations, 56:10–11 (2011), 945–954 , Taylor & Francis
V. Bobkov, Ya. Il'yasov, “Maximal existence domains of positive solutions for two-parametric systems of elliptic equations”, Complex Variables and Elliptic Equations, 61:5 (2016), 587–607 , Taylor & Francis
Ya. Sh. Il'yasov, “On a Procedure of Projective Fibering of Functionals on Banach Spaces”, Proc. Steklov Inst. Math., 232 (2001), 150–156
19.
N. F. Valeev, Ya. Sh. Il'yasov, “On an Inverse Optimization Spectral Problem and a Corresponding Nonlinear Boundary-Value Problem”, Math. Notes, 104:4 (2018), 601–605
20.
Ufa Math. J., 10:4 (2018), 122–128
21.
Ya. Il'yasov, “A duality principle corresponding to the parabolic equations”, Physica D: Nonlinear Phenomena, 237:5 (2008), 692–698 , Elsevier
N. F. Valeev, Y. Sh. Ilyasov, “Inverse spectral problem for Sturm–Liouville operator with prescribed partial trace”, Ufa Math. J., 12:4 (2020), 19–29
25.
Ya. Il'yasov, A. Ivanov, “Computation of maximal turning points to nonlinear equations by nonsmooth optimization”, Optimization Methods and Software, 31:1 (2016), 1–23 , Taylor & Francis
A. A. Ivanov, Ya. Sh. Il'yasov, “Finding bifurcations for solutions of nonlinear equations by quadratic programming methods”, Zh. Vychisl. Mat. Mat. Fiz., 53:3 (2013), 350–364
Ya. Sh. Il'yasov, “On Global Positive Solutions of Parabolic Equations with a Sign-Indefinite Nonlinearity”, Differ. Equ., 41:4 (2005), 548–556
29.
Ya. Sh. Il'yasov, “The Euler functional for equations with the $p$-Laplacian as a function of a spectral parameter”, Proc. Steklov Inst. Math., 214 (1996), 175–186
Ya. Sh. Il'yasov, “On the curve of critical exponents for nonlinear elliptic problems in the case of a zero mass”, Comput. Math. Math. Phys., 57:3 (2017), 497–514
34.
Y. Sh. Il'yasov, E. E. Kholodnov, “On global instability of solutions to hyperbolic equations with non-Lipschitz nonlinearity”, Ufa Math. Journal, 9:4 (2017), 44–53
35.
Ya. Il'yasov, Th. Runst, “An anti-maximum principle for degenerate elliptic boundary value problems with indefinite weights”, Complex Variables and Elliptic Equations, 55:8–10 (2010), 897–910 , Taylor & Francis
Ya. Il'yasov, “On calculation of the bifurcations by the fibering approach”, Harmonic, wavelet and $p$-adic analysis, World Sci. Publ., Hackensack, NJ, 2007, 141–155
Ya. Sh. Il'yasov, “On a condition necessary for the existence of positive solutions to a class of equations with $p$-Laplace operator”, Math. Notes, 66:2 (1999), 249–251
38.
Y. Ilyasov, “Finding Saddle-Node Bifurcations via a Nonlinear Generalized Collatz–Wielandt Formula”, International Journal of Bifurcation and Chaos, 31:1 (2021) , 9 pp. 10.1142/S0218127421500085, arXiv: arXiv:2003.12556, 2020}{arXiv:2003.12556, 2020}
V.Bobkov, P. Drábek, Y. Ilyasov,, “Estimates on the spectral interval of validity of the anti-maximum principle
Journal of Differential Equations”, Journal of Differential Equations, 269:7 (2020) , 20 pp. 10.1016/j.jde.2020.02.020, arXiv: arXiv:1807.06804, 2018}{arXiv:1807.06804, 2018}
Yo. V. Egorov, Ya. Il'yasov, “On conformal invariants for elliptic systems with multiple critical exponents”, Annals of Global Analysis and Geometry, 32:1 (2007), 39–66 , Kluwer Academic Publishers
Ya. Il'yasov, Th. Runst, “On positive solutions of indefinite inhomogeneous Neumann boundary value problems”, Topological Methods in Nonlinear Analysis, 24:1 (2004), 41–67 , Juliusz P. Schauder Centre for Nonlinear Studies
Th. Runst, Ya. Il'yasov, “On equations of the type $Au=g(x,u,Du)$ with degenerate and nonlinear boundary conditions”, Tsukuba J. Math., 23:3 (1999), 505–528
Ya. Sh. Il'yasov, “On asymptotics of solutions to semilinear elliptic equations near the first eigenvalue of the nonperturbed problem”, Math. Notes, 64:4 (1998), 471–475
46.
Ya. Sh. Il'yasov, “On periodic non-trivial solutions of the equation $-\Delta u=g(u)$ in $\mathbb R^{N+1}$”, Izv. Math., 59:1 (1995), 101–119
47.
Ya. Sh. Il'yasov, “An approximation of solutions of “ground state” type of the equations $-\Delta u=g(u)$ in $\mathbf R^{N+1}$”, Differ. Equ., 30:4 (1994), 570–579
48.
Jacques Giacomoni, Yavdat Il'yasov, Deepak Kumar, “On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity”, Asymptotic Analysis, 2024 (to appear) , arXiv: arXiv:2202.12522, 2022
49.
Yavdat Il'yasov, Edcarlos Domingos da Silva, Maxwell Lizete da Silva, “Prescribed energy saddle-point solutions of nonlinear indefinite problems”, Electronic Journal of Differential Equations,, pp.1-11., 23 (2023), 1-11https://hdl.handle.net/10877/16858
Y. Ilyasov, On orbital stability of the physical ground states of the NLS equations, 2021 (Published online) , 21 pp., arXiv: 2103.16353
52.
Yavdat Ilyasov, Rayleigh quotients of the level set manifolds related to the nonlinear PDE, 2021 (to appear) , 20 pp., arXiv: 2108.00891
53.
Marcos LM Carvalho, Yavdat Sh Ilyasov, Carlos Alberto Santos, Separating of critical points on the Nehari manifold via the nonlinear generalized Rayleigh quotients, 2020 (to appear) , 18 pp., arXiv: 1906.07759
54.
Vladimir Bobkov, Pavel Drabek, Yavdat Ilyasov, “On full Zakharov equation and its approximations”, Physica D: Nonlinear Phenomena, 8:23 (2019), 132-168 (Published online) , arXiv: 1801.00803.
55.
Marcos L. M. Carvalho, Yavdat Sh. Ilyasov, Carlos Alberto Santos, Separating of critical points on the Nehari manifold via the nonlinear generalized Rayleigh quotients, 2019 , 18 pp., arXiv: 1906.07759
56.
Y. Ilyasov; K. Silva, “On branches of positive solutions for p-Laplacian problems at the extreme value of Nehari manifold method”, Proceedings of the American Mathematical Society, 146:7 (2018), 2925–2935 doi.org/10.1090/proc/13972, arXiv: arXiv:1704.02477
57.
Yavdat Ilyasov, “On extreme values of Nehari manifold method via nonlinear Rayleighs Quotient”, Topological Methods in Nonlinear Analysis, 49:2 (2017), 683-714
58.
Yavdat Ilyasov, “Bifurcation and blow-up results for equations with $p$-Laplacian and convex-concave nonlinearity”, Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE), 96 (2017), 1-12
59.
Ya. Il'yasov, “On critical exponents curve for nonlinear elliptic equations in zero mass case”, 2016, arXiv: 1605.08142
60.
Ya. Il'yasov, “On extreme values of Nehari manifold method via nonlinear Rayleigh's quotient”, 2015, arXiv: 1509.08019
61.
Ya. Il'yasov, A. Ivanov, “Computation of maximal turning points by a variational approach”, 2014, arXiv: 1404.2810
62.
Vladimir Bobkov, Yavdat Il'yasov, Maximal existence domains of positive solutions for two-parametric systems of elliptic equations, 2014 , 15 pp., arXiv: 1406.5275
63.
Ya. Il'yasov, “Pohozaev’s Identity and Compact Supported Solutions”, The Seventh International Conference on Differential and Functional Differential Equation (Peoples’ Friendship University of Russia, Moscow, Russia, August 22–29, 2014), Peoples' Friendship University of Russia,, Moscow, 2014, 51-52http://dfde2014.mi.ras.ru/
64.
Yavdat Ilyasov, “Precise range for stable and blow-up solutions to equations with p-Laplacian and supercritical nonlinearities”, Abstracts Book. The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 44 (Madrid, Spain, July 07 - July 11, 2014), AIMS, 2014, 189https://www.aimsciences.org/conferences/2014/abstracts-book-finalized-2014-06-10.pdf
65.
Yavdat Ilyasov, “A new geometrical concept in the finding bifurcations. Generalized Collatz-Wielandt formula”, Abstracts Book. The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 33 (Madrid, Spain, July 07 - July 11, 2014), AIMS, 2014, 148https://www.aimsciences.org/conferences/2014/abstracts-book-finalized-2014-06-10.pdf
66.
V. Bobkov, Ya. Il'yasov, “Asymptotic behaviour of branches for ground states of elliptic systems”, Electronic Journal of Differential Equations, 2013:212 (2013), 1–21
67.
Yavdat Il'yasov, “Nehari manifolds and fibering methods. Parametric analysis”, Nonlinear Analysis Plzen 2013 (Pilsen, Czech Republic, August 23-24, 2013), University of West Bohemia, Pilzen, Czech Republic, 2013, 14
68.
Ya. Il'yasov, “The method of the extended functional and solvability of elliptic problems with supercritical exponents”, Lecture Notes of 8Th International Conference on Function Spaces, Differential Operators, Nonlinear Analysis (Fsdona–2011),, 2011
69.
Ya. Il'yasov, “On critical exponent for an elliptic equation with non-ipschitz nonlinearity”, Discrete Contin. Dyn. Syst., 2011, no. Dynamical Systems, Differential Equations and Applications. 8Th Aims Conference. Suppl. Vol. i, 698–706
70.
Yavdat Ilyasov, “Existence of Compactons for Elliptic Equations with Autonomous Nonlinearity”, The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Dresden University of Technology Germany, May 25 - 28, 2010), Dresden University of Technology, 2010, 89https://aimsciences.org/AIMS-Conference/2010/
71.
Ya. Il'yasov, Th. Runst, A. Youssfi, “On the existence of pair positive–negative solutions for resonance problems”, Nonlinear Analysis: Theory, Methods & Applications, 70:10 (2009), 3461–3471 , Elsevier
72.
Ya. S. Il'yasov, “Constructive and algorithmic concept of the bifurcations finding to solutions of the nonlinear equations”, International Conference on Interdisciplinary Mathematical and Statistical Techniques, 2009
73.
Ya. Il'yasov, Yo. Egorov, “Hopf maximum principle violation for elliptic equations with non-Lipschitz nonlinearity”, 2009, arXiv: 0901.4191
74.
Ya. Il'yasov, “Bifurcation Calculus by the Extended Functional Method and Its Applications”, Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems, 2007
75.
Yu. V. Egorov, Ya. Il'yasov, “On multiple solutions for elliptic boundary value problem with two critical exponents”, Harmonic, wavelet and $p$-adic analysis, World Sci. Publ., Hackensack, NJ, 2007, 113–139
76.
Yu. V. Egorov, Ya. Sh. Il'yasov, “On multiple solutions of the Yamabe problem”, Dokl. Akad. Nauk, 409:1 (2006), 19–21
77.
Ya. Il'yasov, N. Sari, “Solutions of minimal period for a Hamiltonian system with a changing sign potential”, Commun. Pure Appl. Anal, 4:1 (2005), 175–185
78.
Ya. Sh. Il'yasov, “Minimax values and parabolic equations with a sign changing nonlinearity”, Dokl. Akad. Nauk, 405:2 (2005), 166–168
79.
Ya. Il'yasov, Th. Runst, “Positive solutions for indefinite inhomogeneous Neumann elliptic problems”, Electronic Journal of Differential Equations, 2003:57 (2003), 1–21 , Texas State University-San Marcos
80.
Ya. Sh. Il'yasov, “The fibering method”, Nonlinear analysis and nonlinear differential equations (ussian), FizMatLit, Moscow, 2003, 197–243
81.
Ya. Il'yasov, Th. Runst, “Nonlocal investigations of inhomogeneous indefinite elliptic equations via variational methods”, Function spaces, differential operators and nonlinear analysis (eistungen, 2001), Birkhäuser, Basel, 2003, 342–352
82.
Ya. Sh. Il'yasov, “On nonlocal investigations of families of elliptic equations with convex-concave nonlinearities”, Dokl. Akad. Nauk, 392:5 (2003), 603–605
83.
Ya. Sh. Il'yasov, “The Pokhozhaev Identity and the Fibering Method”, Differ. Equ., 38:10 (2002), 1453–1459
84.
Ya. Il'yasov, “On positive solutions of indefinite elliptic equations”, Comptes Rendus de l'Acad mie des Sciences-Series I-Mathematics, 333:6 (2001), 533–538 , Elsevier
85.
Ya. Sh. Il'yasov, T. Runst, “On the existence of multiple positive solutions for a class of nonlinear eumann boundary value problems”, Dokl. Akad. Nauk, 376:3 (2001), 300–302
86.
Ya. Il'yasov, “Action as function of period for ground states of semilinear elliptic equations”, NoDEA Nonlinear Differential Equations Appl., 7:4 (2000), 369–387
87.
Ya. Il'yasov, Th. Runst, “Existence and uniqueness theorems for equations of the type $Au(x)=g(x,u,Du)$ with degenerate and nonlinear boundary conditions”, Function spaces, differential operators and nonlinear analysis (udasjärvi, 1999), Acad. Sci. Czech Repub., Prague, 2000, 143–148
Ya. Sh. Il'yasov, “On the existence of conformally equivalent metrics for Riemannian manifolds with boundary”, Differ. Equ., 35:3 (1999), 335–340
90.
Ya. Sh. Il'yasov, “On the manifold of solutions of semilinear elliptic equations satisfying the Pokhozhaev identity. II”, Differ. Equ., 33:12 (1997), 1673–1678
91.
Ya. Sh. Il'yasov, “On the manifold of solutions of semilinear elliptic equations satisfying the Pokhozhaev identity. I”, Differ. Equ., 32:8 (1996), 1067–1074
92.
Ya. Sh. Il'yasov, “An equation that arises in studying ground state solutions to semilinear elliptic equations”, Math. Notes, 58:3 (1995), 996–1000
93.
Ya. Sh. Il'yasov, “On function of action on the manifold of ground state solutions”, Theoret. and Math. Phys., 105:3 (1995), 1546–1555
94.
Ya. Sh. Il'yasov, “On existence and non-existence of periodic solutions for the equations $-\Delta u=g(u)$ in $\bold R\sp {N+1}$”, Dynam. Systems Appl., 4:4 (1995), 529–548
95.
Ya. Sh. Il'yasov, “On the manifold of solutions of “ground state” type of semilinear elliptic equations”, Dokl. Akad. Nauk, 342:4 (1995), 452–454
96.
Ya. Sh. Ilyasov, “Existence of periodic nonnegative solutions of the equations $-\!\Delta u=g(u)$ in $\mathbb{R}^{N+1}$”, Dokl. Math., 48:2 (1994), 278–281
97.
Y. Sh. Il'yasov, “Non-equilibrium phase transitions in the multicomponent chemical systems”, Unsteady State Processes in Catalysis: Proceedings of the International Conference, Novosibirsk, eds. Yu S. Matros, VSP BV, Zeist, Netherlands, 1990, 123-126
98.
Ilyasov, Yavdat Shavkatovich., Ob asimptoticheskikh razlozheniyakh reshenii kvazilineinykh stokhasticheskikh parabolicheskikh uravnenii, Diss. kand. fiz.-matem. nauk, AN SSSR. Ural. otd-nie. Bashk. nauch. tsentr. In-t matematiki s VTs, Ufa, 1988 , 149 pp. http://search.rsl.ru/ru/record/01008474354
99.
Ya. Sh. Il'yasov, A. I. Komech, “Girsanov's theorem and ergodic properties of statistical solutions of nonlinear parabolic equations”, Trudy Sem. Petrovsk., 1987, no. 12, 88–117, 243–244
100.
Ya. Sh. Il'yasov, “Asymptotic expansion of solutions of nonlinear stochastic parabolic equations”, Izv. Akad. Nauk Azerbaĭdzhan. SSR Ser. Fiz.-Tekhn. Mat. Nauk, 7:2 (1986), 36–40
101.
Ya. Sh. Il'yasov, “Asymptotic expansion of the solutions of nonlinear parabolic equations with a small parameter in the presence of white noise”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1986, no. 3, 101–104, 121
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