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

doi:10.1007/s10473-021-0304-0

Abstract

Abstract: We are concerned with the nonlinear Schrödinger-Poisson equation \begin{equation} \tag{P} \left\{\begin{array}{ll} -\Delta u +(V(x) -\lambda)u+\phi (x) u =f(u), \\ -\Delta\phi = u^2,\ \lim\limits_{|x|\rightarrow +\infty}\phi(x)=0, \ \ \ x\in \mathbb{R}^3, \end{array}\right. \end{equation} where $\lambda$ 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

Yongsheng JIANG, Na WEI, Yonghong WU. MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER-POISSON EQUATION WITH A GENERAL NONLINEARITY[J].Acta mathematica scientia,Series B, 2021, 41(3): 703-711.

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