Lixia WANG , Shiwang MA , Na XU . MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL[J]. Acta mathematica scientia, Series B, 2017 , 37(2) : 555 -572 . DOI: 10.1016/S0252-9602(17)30021-8

[1] Ackermann N. A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations. J Funct Anal, 2006, 234:277-320
[2] Alves C O, Carrião P C, Medeiros E S. Multiplicity of solutions for a class of quasilinear problem in exterior domains with Neumann conditions. Abstr Appl Anal, 2004, 3:251-268
[3] Ambrosetti A, Ruiz D. Multiple bound states for the Schrödinger-Poisson equation. Commun Contemp Math, 2008, 10:391-404
[4] Azzollini A, Pomponio A. Ground state solutions for the nonlinear Schrödinger-Maxwell equations. J Math Anal Appl, 2008, 345:90-108
[5] Bartsch T, Wang Z Q. Existence and multiplicity results for some superlinear elliptic problem on RN. Comm Partial Differ Equat, 1995, 20:1725-1741
[6] Benci V, Fortunato D. An eigenvalue problem for the Schrödinger-Maxwell equations. Topol Methods Nonlinear Anal, 1998, 11(2):283-293
[7] Brezis H, Lieb E H. A relation between pointwise convergence of functions and convergence functionals. Proc Amer Math Soc, 1983, 8:486-490
[8] Coclite G M. A multiplicity result for the nonlinear Schrödinger-Maxwell equations. Commun Appl Anal, 2003, 7(2/3):417-423
[9] Coclite G M. A multiplicity result for the Schrödinger-Maxwell equations with negative potential. Ann Polon Math, 2002, 79(1):21-30
[10] Chen S J, Tang C L. High energy solutions for the superlinear Schrödinger-Maxwell equations. Nonlinear Anal, 2009, 71:4927-4934
[11] Chen S J, Tang C L. Multiple solutions for a non-homogeneous Schrödinger-Maxwell and Klein-GordonMaxwell equations on R3. Nonlinear Differ Equat Appl, 2010, 17:559-574
[12] DAprile T, Mugnai D. Non-existence results for the coupled Klein-Gordon-Maxwell equations. Adv Nonlinear Stud, 2004, 4(3):307-322
[13] DAprile T, Mugnai D. Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations. Proc Roy Soc Edinburgh Sect A, 2004, 134:893-906
[14] Ding L, Li L, Zhang J L. Mulltiple solutions for nonhomogeneous Schrödinger-Poisson system with asymptotical nonlinearity in R3. Taiwanese Journal of Mathematics, 2013, 17(5):1627-1650
[15] Ding Y H, Szulkin A. Bound states for semilinear Schrödinger equations with sign-changing potential. Calc Var Partial Differ Equat, 2007, 29:397-419
[16] Du M, Zhang F B. Existence of positive solutions for a nonhomogeneous Schrödinger-Poisson system in R3. International Journal of Nonlinear Science, 2013, 16(2):185-192
[17] Jiang Y S, Wang Z P, Zhou H S. Multiple solutions for a nonhomogeneous Schrödinger-Maxwell system in R3. Nonlinear Anal, 2013, 83:50-57
[18] Kikuchi H. On the existence of a solution for elliptic system related to the Maxwell-Schrödinger equations. Nonlinear Anal, 2007, 67(5):1445-1456
[19] Mawhin J, Willem M. Critical Point Theory and Hamiltonian Systems. Berlin:Springer, 1989
[20] Mercuri C. Positive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity. (English summary) Atti Accad Naz Lincei Cl Sci Fis Mat Natur Rend Lincei (9) Mat Appl, 2008, 19(3):211-227
[21] Rabinowitz P H. Minimax Methods in Critical Point Theory with Applications to Differential Equations. Providence:Amer Math Soc, 1986
[22] Ruiz D. The Schrödinger-Poisson equation under the effect of a nonlinear local term. J Funct Anal, 2006, 237(2):655-674
[23] Salvatore A. Multiple solitary waves for a non-homogeneous Schrödinger-Maxwell system in R³. Adv Nonlinear Stud, 2006, 6(2):157-169
[24] Struwe M. Variational Methods:Applications to Nonlinear Partial Differential Equations and Hamiltonian systems. 3rd ed. Berlin:Springer, 2000
[25] Sun J T. Infinitely many solutions for a class of sublinear Schrödinger-Maxwell equations. J Math Anal Appl, 2012, 390:514-522
[26] Sun M Z, Su J B, Zhao L G. Infinitely many solutions for a Schrödinger-Poisson system with concave and convex nonlinearities. Discrete Contin Dyn Syst, 2015, 35:427-440
[27] Sun J T, Wu T F. Existence and multiplicity of positive solutions for a Schrödinger-Poisson system with a perturbation. Topological Methods in Nonlinear Analysis, 2015, 46:967-998
[28] Sun J T, Wu T F. On the nonlinear Schrödinger-Poisson system with sign-changing potential. Z Angew Math Phys, 2015, 66:1649-1669
[29] Wang Z P, Zhou H S. Positive solutions for a nonlinear stationary Schrödinger-Poisson system in R³. Discrete Contin Dyn Syst, 2007, 18:809-816
[30] Willem M. Minimax Theorems. Boston:Birkhäuser, 1996
[31] Willem M. Analyse Harmonique Réelle. Paris:Hermann, 1995
[32] Wu T F. Multiplicity results for a semi-linear elliptic equation involving sign-changing weigh function. Rocky Mountain J Mathematics, 2009, 39(3):995-1011
[33] Wu T F. Four positive solutions for a semilinear elliptic equation involving concave and convex nonlinearities. Nonlinear Anal, 2009, 70:1377-1392
[34] Wu T F. The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions. Nonlinear Anal, 2008, 68:1733-1745
[35] Ye Y W, Tang C L. Existence and multiplicity of solutions for Schrödinger-Poisson equations with signchanging potential. Calc Var, 2015, 53:383-411
[36] Zhao L G, Zhao F K. Positive solutions for Schrödinger-Poisson equations with a critical exponent. Nonlinear Anal, 2009, 70:2150-2164
[37] Zhao L G, Zhao F K. On the existence of solutions for the Schrödinger-Poisson equations. J Math Anal Appl, 2008, 346(1):155-169
[38] Zhao L G, Liu H D, Zhao F K. Existence and concentration of solutions for the Schrödinger-Poisson equations with steep well potential. J Differ Equat, 2013, 255:1-23