On sign-changing solutions for quasilinear Schrödinger-Poisson system with critical growth

References

• Illner R, Kavian O, Lange H. Stationary solutions of quasi-Linear Schrödinger-Poisson system. J Differ Equ. 1998;145:1–16.
   Web of Science ®Google Scholar
• Feng X, Zhang Y. Existence of non-trivial solution for a class of modified Schrödinger-Poisson equations via perturbation method. J Math Anal Appl. 2016;442:673–684.
   Web of Science ®Google Scholar
• Wang Z, Zhou H. Positive solution for a nonlinear stationary Schrödinger-Poisson system in R3. Discrete Contin Dyn Syst. 2012;18:809–816.
   Google Scholar
• Zhao L, Liu H, Zhao F. Existence and concentration of solutions for the Schrödinger-Poisson equations with steep well potential. J Differ Equ. 2013;255:1–23.
   Web of Science ®Google Scholar
• D'Aprile T, Mugnai D. Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations. Proc Roy Soc Edinburgh Sect A. 2004;134:893–906.
   Google Scholar
• Ianni I. Sign-changing radial solutions for the Schröodinger-Poisson-Slater problem. Topol Methods Nonlinear Anal. 2013;41:365–385.
   Web of Science ®Google Scholar
• Ruiz D. On the Schrödinger-Poisson-Slater system: behavior of minimizers, radial and nonradial cases. Arch Ration Mech Anal. 2010;198:349–368.
   Web of Science ®Google Scholar
• Ambrosetti A, Ruiz D. Multiple bound states for the Schrödinger-Poisson problem. Commun Contemp Math. 2008;10:391–404.
   Web of Science ®Google Scholar
• Colin GM. A multiplicity result for nonlinear Schrödinger-Maxwell equation. Commun Appl Anal. 2003;7:417–423.
   Google Scholar
• Li G, Peng S, Yan S. Infinitely many positive solutions for the nonlinear Schrödinger-Poisson system. Commun Contemp Math. 2010;12:1069–1092.
   Web of Science ®Google Scholar
• Liu Z, Wang Z, Zhang J. Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system. Ann Mat Pura Appl. 2016;4:775–794.
   Google Scholar
• Li W, Rădulescu V, Zhang BL. Infinitely many solutions for fractional Kirchhoff-Schrödinger-Poisson systems. J Math Phys. 2019;60:011506.
   Google Scholar
• Alves CO, Souto MAS, Soares SHM. Schrödinger-Poisson equations without Ambrosetti-Rabinowitz condition. J Math Anal Appl. 2011;377:584–592.
   Web of Science ®Google Scholar
• Azzollini A, Pomponio A. Ground state solutions for the nonlinear Schrödinger-Maxwell equations. J Math Anal Appl. 2008;345:90–108.
   Web of Science ®Google Scholar
• Sun J, Ma S. Ground state solutions for some Schrödinger-Poisson systems with periodic potentials. J Differ Equ. 2016;260:2119–2149.
   Web of Science ®Google Scholar
• D'Aprile T, Wei JC. On bound states concentrating on sphere for the Maxwell-Schrödinger equations. SIAM J Math Anal. 2005;15:321–342.
   Google Scholar
• Ianni I, Varia G. Solutions of the Schrödinger-Poisson problem concentrating on spheres, part I: necessary condition. Math Models Methods Appl Sci. 2009;19:707–720.
   Web of Science ®Google Scholar
• Ianni I. Solutions of the Schrödinger-Poisson problem concentrating on spheres, part II: existence. Math Models Methods Appl Sci. 2009;19:877–910.
   Web of Science ®Google Scholar
• Chen S, Tang X. Ground state sign-changing solutions for a class of Schrödinger-Poisson type problems in R3. Z Angew Math Phys. 2016;67:102. 18 pp.
   Web of Science ®Google Scholar
• Wang D, Ma Y, Guan W. Least energy sign-changing solutions for the fractional Schrödinger-Poisson systems in R3. Bound Value Probl. 2019;2019:25.
   Web of Science ®Google Scholar
• Wang D, Zhang H, Guan W. Existence of least-energy sign-changing solutions for Schrödinger-Poisson system with critical growth. J Math Anal Appl. 2019;479:2284–2301.
   Web of Science ®Google Scholar
• Chen L, Feng X, Hao X. The existence of sign-changing solution for a class of quasilinear Schrödinger-Poisson systems via perturbation method. Bound Value Probl. 2019;2019:159.
   Web of Science ®Google Scholar
• Benmilh K, Kavian O. Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger-Poisson systems in R3. Ann Inst H Poincaré Anal Non Linéaire. 2008;25:449–470.
   Web of Science ®Google Scholar
• Ding L, Lin L, Meng YJ, et al. Existence and asymptotic behavior of ground state for Quasilinear Schrödinger-Poisson system in R3. Topol Methods Nonlinear Anal. 2016;47:241–264.
   Web of Science ®Google Scholar
• Figueiredo GM, Siciliano G. Existence and asymptotic behaviour of solutions for a quasi-linear Schrödinger-poisson system under a critical nonlinearity, arXiv:1707.05353. 2017.
   Google Scholar
• Figueiredo GM, Siciliano G. Quasi-linear Schrödinger-Poisson system under an exponential critical nonlinearity: existence and asymptotic behaviour of solutions. Arch Math. 2019;112:313–327.
   Web of Science ®Google Scholar
• Mao AM, Chang HJ. Schrödinger-Poisson system with radial potentials and discontinuous Quasilinear nonlinearity. Topol Methods Nonlinear Anal. 2018;51:79–89.
   Web of Science ®Google Scholar
• Shen LJ. Ground state solutions for a class of generalized quasilinear Schrödinger-Poisson systems. Bound Value Probl. 2018;2018:44.
   Google Scholar
• Bartsch T, Weth T. Three nodal solutions of singularly perturbed elliptic equations on domains without topology. Ann Inst H Poincaré Anal Non Linéaire. 2005;22:259–281.
   Web of Science ®Google Scholar
• Liu X, Liu J, Wang Z. Quasilinear elliptic equations via perturbation method. Proc Am Math Soc. 2013;141:253–263.
   Web of Science ®Google Scholar
• Miranda C. Un'osservazione su un teorema di Brouwer. Boll Unione Mat Ital. 1940;3:5–7.
   Google Scholar
• Chen S, Liu J, Wu X. Existence and multiplicity of nontrivial solutions for a class of modified nonlinear fourth-order elliptic equations on RN. Appl Math Comput. 2014;248:593–601.
   Web of Science ®Google Scholar
• Willem M. Minimax theorems. Boston (MA): Birkhäuser; 1996.
   Google Scholar
• Zhang W, Liu X. Infinitely many sign-changing solutions for a quasilinear elliptic equation in RN. J Math Anal Appl. 2015;427:722–740.
   Web of Science ®Google Scholar