Ground states for planar Hamiltonian elliptic systems with critical exponential growth
Tài liệu tham khảo
Adimurthi, 1990, Multiplicity results for semilinear elliptic equations in bounded domain of R2 involving critical exponent, Ann. Sc. Norm. Super. Pisa, 17, 481
Albuquerque, 2016, On a class of Hamiltonian elliptic systems involving unbounded or decaying potentials in dimension two, Math. Nachr., 289, 1568, 10.1002/mana.201400203
Ávila, 2003, On the existence and shape of least energy solutions for some elliptic systems, J. Differ. Equ., 191, 348, 10.1016/S0022-0396(03)00017-2
Bartolo, 1983, Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity, Nonlinear Anal., 7, 981, 10.1016/0362-546X(83)90115-3
Bartsch, 1999, Infinitely many solutions of nonlinear elliptic systems, Prog. Nonlinear Differ. Equ. Appl., 35, 51
Benci, 1979, Critical point theorems for indefinite functionals, Invent. Math., 52, 241, 10.1007/BF01389883
Bonheure, 2012, Ground state and non-ground state solutions of some strongly coupled elliptic systems, Trans. Am. Math. Soc., 364, 447, 10.1090/S0002-9947-2011-05452-8
Bonheure, 2014, Hamiltonian elliptic systems: a guide to variational frameworks, Port. Math., 71, 301, 10.4171/PM/1954
Busca, 2000, Symmetry results for semilinear elliptic systems in the whole space, J. Differ. Equ., 163, 41, 10.1006/jdeq.1999.3701
Cassani, 2015, Existence of solitary waves for supercritical Schrödinger systems in dimension two, Calc. Var. Partial Differ. Equ., 54, 1673, 10.1007/s00526-015-0840-3
Cao, 1992, Nontrivial solution of semilinear elliptic equation with critical exponent in R2, Commun. Partial Differ. Equ., 17, 407, 10.1080/03605309208820848
Cerami, 1980, On the existence of eigenvalues for a nonlinear boundary value problem, Ann. Mat. Pura Appl., 124, 161, 10.1007/BF01795391
Chen, 2020, Axially symmetric solutions for the planar Schrödinger-Poisson system with critical exponential growth, J. Differ. Equ., 269, 9144, 10.1016/j.jde.2020.06.043
Chen, 2021, Improved results on planar Kirchhoff-type elliptic problems with critical exponential growth, Z. Angew. Math. Phys., 72, 38, 10.1007/s00033-020-01455-w
Chen, 2021, On the planar Schrödinger equation with indefinite linear part and critical growth nonlinearity, Calc. Var. Partial Differ. Equ., 60, 95, 10.1007/s00526-021-01963-1
Clement, 1992, Positive solutions of semilinear elliptic systems, Commun. Partial Differ. Equ., 17, 923, 10.1080/03605309208820869
Costa, 1996, A unified approach to strongly indefinite functionals, J. Differ. Equ., 122, 521, 10.1006/jdeq.1996.0039
de Figueiredo, 1995, Elliptic equations in R2 with nonlinearities in the critical growth range, Calc. Var. Partial Differ. Equ., 3, 139, 10.1007/BF01205003
de Figueiredo, 2005, An Orlicz-space approach to superlinear elliptic systems, J. Funct. Anal., 224, 471, 10.1016/j.jfa.2004.09.008
de Figueiredo, 2004, Critical and subcritical elliptic systems in dimension two, Indiana Univ. Math. J., 53, 1037, 10.1512/iumj.2004.53.2402
de Figueiredo, 2011, Elliptic equations and systems with critical Trudinger-Moser nonlinearities, Discrete Contin. Dyn. Syst., 30, 455, 10.3934/dcds.2011.30.455
de Figueiredo, 2020, Ground state solutions of Hamiltonian elliptic systems in dimension two, Proc. R. Soc. Edinb., 150, 1737, 10.1017/prm.2018.78
de Figueiredo, 1998, Decay, symmetry and existence of solutions to semilinear elliptic systems, Nonlinear Anal., 33, 211, 10.1016/S0362-546X(97)00548-8
de Souza, 2016, Hamiltonian elliptic systems in R2 with subcritical and critical exponential growth, Ann. Math., 195, 935
Ding, 2007, vol. 7
Ding, 2006, Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms, J. Differ. Equ., 222, 137, 10.1016/j.jde.2005.03.011
do Ó, 2021, Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions, Discrete Contin. Dyn. Syst., 41, 277, 10.3934/dcds.2020138
Hulshof, 1993, Differential systems with strongly indefinite variational structure, J. Funct. Anal., 114, 32, 10.1006/jfan.1993.1062
Kryszewski, 1998, Generalized linking theorem with an application to a semilinear Schrödinger equation, Adv. Differ. Equ., 3, 441
Lam, 2014, Elliptic equations and systems with subcritical and critical exponential growth without the Ambrosetti-Rabinowitz condition, J. Geom. Anal., 24, 118, 10.1007/s12220-012-9330-4
Lions, 1984, The concentration-compactness principle in the calculus of variations. The locally compact case I, II, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 1, 109, 10.1016/s0294-1449(16)30428-0
Pankov, 2005, Periodic nonlinear Schröinger equation with application to photonic crystals, Milan J. Math., 73, 259, 10.1007/s00032-005-0047-8
Qin, 2021, On the planar Choquard equation with indefinite potential and critical exponential growth, J. Differ. Equ., 285, 40, 10.1016/j.jde.2021.03.011
Sirakov, 2010, Soliton solutions to systems of coupled Schrödinger equations of Hamiltonian type, Trans. Am. Math. Soc., 362, 5729, 10.1090/S0002-9947-2010-04982-7
Szulkin, 2009, Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257, 3802, 10.1016/j.jfa.2009.09.013
Tang, 2015, Non-Nehari manifold method for asymptotically periodic Schrödinger equations, Sci. China Math., 58, 715, 10.1007/s11425-014-4957-1
Tang, 2020, Existence of ground state solutions of Nehari-Pankov type to Schrödinger systems, Sci. China Math., 63, 113, 10.1007/s11425-017-9332-3
van der Vorst, 1992, Variational identities and applications to differential systems, Arch. Ration. Mech. Anal., 116, 375, 10.1007/BF00375674
Willem, 1996
Zhao, 2013, On ground state solutions for superlinear Hamiltonian elliptic systems, Z. Angew. Math. Phys., 64, 403, 10.1007/s00033-012-0258-0
