Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 703-711.doi: 10.1007/s10473-021-0304-0

• Articles • Previous Articles     Next Articles

MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER-POISSON EQUATION WITH A GENERAL NONLINEARITY

Yongsheng JIANG1, Na WEI1, Yonghong WU2   

  1. 1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China;
    2. Department of Mathematics and Statistics, Curtin University, GPO Box U 1987, WA 6845, Australia
  • Received:2019-09-03 Revised:2020-05-02 Online:2021-06-25 Published:2021-06-07
  • Contact: Na WEI E-mail:nawei2006@126.com
  • About author:Yongsheng JIANG,E-mail:jiangys@zuel.edu.cn;Yonghong WU,E-mail:Y.Wu@curtin.edu.au
  • Supported by:
    This research was supported by NSFC (11871386 and 12071482) and the Natural Science Foundation of Hubei Province (2019CFB570).

Abstract: We are concerned with the nonlinear Schrödinger-Poisson equation {Δu+(V(x)λ)u+ϕ(x)u=f(u),Δϕ=u2, lim|x|+ϕ(x)=0,   xR3,

where λ is a parameter, V(x) is an unbounded potential and f(u) is a general nonlinearity. We prove the existence of a ground state solution and multiple solutions to problem (P).

Key words: Multiple solutions, ground state solution, Schr?dinger-Poisson equation

CLC Number: 

  • 35J20
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