[1] Ackermann N. On a periodic Schrödinger equation with nonlocal superlinear part. Math Z, 2004, 248: 423-443
[2] Alves C, Mukherjee T. Existence and multiplicity of solutions for a class of Hamiltonian systems. Monatsh Math, 2020, 192: 269-289
[3] Bartsch T, Ding Y. Deformation theorems on non-metrizable vector spaces and applications to critical point theory. Math Nachr, 2006, 279: 1267-1288
[4] Bartsch T, Ding Y. On a nonlinear Schrödinger equation with periodic potential. Math Ann, 1999, 313: 15-37
[5] Bartsch T, de Figueiredo D. Infinitely many solutions of nonlinear elliptic systems. Progress in Nonlinear Differential Equations and Their Applications, 1999, 35: 51-67
[6] Batkam C. On a superquadratic elliptic system with strongly indefinite structure. Appl Math Comput, 2014, 233: 243-251
[7] Bernini F, Bieganowski B. Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities. Calc Var Partial Differential Equations, 2022, 61: Art 182
[8] Bieganowski B.Schrödinger-type equations with sign-changing nonlinearities: A survey. arXiv:1810.01754
[9] Bonheure D, Denis, Santos E, Tavares H. Hamiltonian elliptic systems: a guide to variational frameworks. Port Math, 2014, 71(3): 301-395
[10] Cassani D, Tarsi C. Existence of solitary waves for supercritical Schrödinger systems in dimension two.Calc Var Partial Differential Equations, 2015, 54: 1673-1704
[11] Chen S, Tang X. On the planar Schrödinger equation with indefinite linear part and critical growth nonlinearity. Calc Var Partial Differential Equations, 2021 60(3): Art 95
[12] Chen J, Zhang Q. Ground state solution for strongly indefinite Choquard system. Nonlinear Anal, 2022 220: 112855
[13] Chen S, Wang C. An infite-dimensional linking theorem without upper semi-continuous assumption and its applications. J Math Anal Appl, 2014 420: 1552-1567
[14] Coti Zelati V, Rabinowitz P. Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. J Amer Math Soc, 1991 4: 693-727
[15] Coti Zelati V, Rabinowitz P. Homoclinic type solutions for a semilinear elliptic PDE on $\mathbb{R}^ n$. Comm Pure Appl Math, 1992, 45: 1217-1269
[16] de Figueiredo D. Semilinear elliptic systems: existence, multiplicity, symmetry of solutions. Handbook of Differential Equations: Stationary Partial Differential Equations, 2008, 5: 1-48
[17] De Figueiredo D, do Ó J, Zhang J. Ground state solutions of Hamiltonian elliptic systems in dimension two. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2020, 150(4): 1737-1768
[18] De Figueiredo D, Felmer P. On superquadratic elliptic systems. Trans Amer Math Soc, 1994, 102: 188-207
[19] Ding Y, Lee C. Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms. J Differential Equations, 2006, 222: 137-163
[20] Furtado M, de Marchi R. Asymptotically periodic superquadratic Hamiltonian system. J Math Anal Appl, 2016, 433: 712-731
[21] Gu L. Multiple solutions for a Choquard system with periodic potential. J Math Anal Appl, 2020, 484: 123704
[22] Gu L, Zhou H. An improved fountain theorem and its application. Adv Nonlinear Stud, 2017, 17: 727-738
[23] Han P. Strongly indefinite systems with critical Sobolev exponents and weights. Appl Math Lett, 2004, 17: 909-917
[24] Hulshof J, Vandervorst R. Differential systems with strongly indefinite variational structure. J Funct Anal, 1993, 114: 32-58
[25] Kryszewski W, Szulkin A. Generalized linking theorem with an application to semilinear Schrödinger equation. Adv Differential Equations, 1998, 3: 441-472
[26] Kuchment P.The mathematics of photonic crystals// Bao G, Cowsar L, Masters W. Math Model Opt Sci. Philadephia: SIAM, 2001: 207-272
[27] Leuyacc Y, Soares S. On a Hamiltonian system with critical exponential growth. Milan J Math, 2019, 87 105-140
[28] Li G, Szulkin A. An asymptotically periodic Schrödinger equation with indefinite linear part. Commun Contemp Math, 2002, 4: 763-776
[29] Li G, Yang J. Asymptotically linear elliptic systems. Comm Partial Differential Equations, 2004, 29: 925-954
[30] Li G, Wang C. Multiple solutions for a semilinear elliptic system in $\mathbb{R}^N$. Math Meth Appl Sci, 2013, 18 (36): 2456-2466
[31] Li G, Wang C. The existence of nontrivial solutions to a semilinear elliptic system on $\mathbb{R}^N$ without the Ambrosetti-Rabinowitz condition. Acta Math Sci, 2010, 30B(6): 1917-1936
[32] Liao F, Tang X, Zhang J. Existence of solutions for periodic elliptic system with general superlinear nonlinearity. Z Angew Math Phys, 2015, 66: 689-701
[33] Liao F, Zhang W. New asymptotically quadratic conditions for Hamiltonian elliptic systems. Adv Nonlinear Anal, 2022, 11: 469-481
[34] Liu Z. Infinitely many solutions for elliptic systems with strongly indefinite variational structure. Acta Math Sci, 2010, 30B(1): 55-64
[35] Nie W. Optical nonlinearity: phenomena, applications,materials. Adv Mater, 1993, 5: 520-545
[36] Pankov A. Periodic nonlinear Schrödinger equation with application to photonic crystals. Milan J Math, 2005, 73 : 259-287
[37] Ruf B. Superlinear elliptic equations and systems. Handbook of Differential Equations: Stationary Partial Differential Equations, 2008, 5: 211-276
[38] Soares S, Leuyacc Y. Hamiltonian elliptic systems in dimension two with potentials which can vanish at infinity. Commun Contemp Math, 2018, 20(8): 1750053
[39] Sun J, Chen H, Chu J. On periodic Hamiltonian elliptic systems with spectrum point zero. Math Nachr, 2012, 285(17/18): 2233-2251
[40] Tang X, Lin X, Yu J. Nontrivial solutions for Schrödinger equation with local super-quadratic conditions. J Dynam Differential Equations, 2019, 31(1): 369-383
[41] Tang X, Chen S, Lin X, Yu J. Ground state solutions of Nehari-Pankov type for Schrödinger equations with local super-quadratic conditions. J Differ Equ, 2020, 268: 4663-4690
[42] Tang X, Chen S. Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials. Calc Var Partial Differential Equations, 2017, 55: Art 110
[43] Toon E, Ubilla P. Hamiltonian systems of Schrödinger equations with vanishing potentials. Commun Contemp Math, 2022, 24(1): 2050074
[44] Zhang R, Chen J, Zhao F. Multiple solutions for superlinger elliptic systems of Hamiltonian type. Discrete Contin Dyn Syst, 2011, 30: 1249-1262
[45] Zhao F, Zhao L, Ding Y. A note on superlinear Hamiltonian elliptic systems. J Math Phys, 2009, 50: 112702
[46] Zhao F, Zhao L, Ding Y. Multiple solutions for a superlinear and periodic wlliptic system on $\mathbb{R}^N$. Z Angew Math Phys, 2011, 62: 495-511
[47] Zhao F, Zhao L, Ding Y. Multiple solutions for asymptotically linear elliptic systems. NoDEA Nonlinear Differential Equations Appl, 2008, 15: 673-688