Existence and multiplicity results for the nonlinear Schrodinger-Poisson systems

被引：36

作者：

Yang, Ming-Hai ^{[1
]}

Han, Zhi-Qing ^{[2
]}

机构：

[1] Xinyang Normal Univ, Dept Math, Xinyang 464000, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2012年 / 13卷 / 03期

关键词：

Schrodinger-Poisson system; Mountain pass theorem; Fountain theorem; Variational methods; POSITIVE SOLUTIONS; ELLIPTIC PROBLEMS; BOUND-STATES; EQUATIONS; MAXWELL; THEOREMS;

D O I：

10.1016/j.nonrwa.2011.07.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the existence and multiplicity results for the nonlinear Schrodinger-Poisson systems {-Delta u + V(x)u K(x)phi(x)u = f(x, u), in R-3 -Delta phi = K (x)u(2), in R-3. (*) Under certain assumptions on V. K and f, we obtain at least one nontrivial solution for (*) without assuming the Ambrosetti and Rabinowitz condition by using the mountain pass theorem, and obtain infinitely many high energy solutions when f (x,.) is odd by using the fountain theorem. (C) 2011 Published by Elsevier Ltd

引用

页码：1093 / 1101

页数：9

共 50 条

[41] Multiple positive bound states for critical Schrodinger-Poisson systems
Cerami, Giovanna
Molle, Riccardo
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2019, 25
[42] The existence and concentration of positive solutions for a nonlinear Schrodinger-Poisson system with critical growth
Zhang, Jianjun
JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (03)
[43] Existence and uniqueness of constraint minimizers for the planar Schrodinger-Poisson system with logarithmic potentials
Guo, Yujin
Liang, Wenning
Li, Yan
JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 369 : 299 - 352
[44] Multiplicity and Concentration Results for Fractional Schrodinger-Poisson Equations with Magnetic Fields and Critical Growth
Ambrosio, Vincenzo
POTENTIAL ANALYSIS, 2020, 52 (04) : 565 - 600
[45] Existence and multiplicity of normalized solutions for a class of fractional Schrodinger-Poisson equations
Yang, Zhipeng
Zhao, Fukun
Zhao, Shunneng
ANNALES FENNICI MATHEMATICI, 2022, 47 (02): : 777 - 790
[46] Existence, uniqueness and multiplicity of positive solutions for Schrodinger-Poisson system with singularity
Zhang, Qi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 437 (01) : 160 - 180
[47] Existence of solutions to a class of Schrodinger-Poisson systems with indefinite nonlinearity
Li, Fuyi
Chang, Caihong
Feng, Xiaojing
APPLICABLE ANALYSIS, 2017, 96 (05) : 721 - 740
[48] Multiplicity of solutions for a class of critical Schrodinger-Poisson systems on the Heisenberg group
Li, Shiqi
Song, Yueqiang
OPEN MATHEMATICS, 2023, 21 (01):
[49] Existence and stability results for the planar Schrodinger-Poisson system
Zhang, Guoqing
Guo, Wenyan
Zhang, Weiguo
ARCHIV DER MATHEMATIK, 2016, 107 (05) : 561 - 568
[50] Existence and Uniqueness of Multi-Bump Solutions for Nonlinear Schrodinger-Poisson Systems
Yu, Mingzhu
Chen, Haibo
ADVANCED NONLINEAR STUDIES, 2021, 21 (03) : 661 - 681

← 1 2 3 4 5 →