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Multiple Solutions for the Schrödinger-Poisson Equation with a General Nonlinearity

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Abstract

We are concerned with the nonlinear Schrödinger-Poisson equation

$$\begin{cases}-\Delta u+(V(x)-\lambda)u+\phi(x)u=f(u),\\-\Delta\phi=u^{2},\lim\limits_{\vert x\vert\rightarrow+\infty}\phi(x)=0,x\in \mathbb{R}^{3},\end{cases}\ {\mathrm{(P)}}$$

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).

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Authors and Affiliations

  1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Yongsheng Jiang  (蒋永生) & Na Wei  (魏娜)

  2. Department of Mathematics and Statistics, Curtin University, GPO Box U 1987, Perth, WA, 6845, Australia

    Na Wei  (魏娜) & Yonghong Wu  (吴永洪)

Authors
  1. Yongsheng Jiang  (蒋永生)
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  2. Na Wei  (魏娜)
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  3. Yonghong Wu  (吴永洪)
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Corresponding author

Correspondence to Na Wei  (魏娜).

Additional information

This research was supported by NSFC (11871386 and 12071482) and the Natural Science Foundation of Hubei Province (2019CFB570).

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Jiang, Y., Wei, N. & Wu, Y. Multiple Solutions for the Schrödinger-Poisson Equation with a General Nonlinearity. Acta Math Sci 41, 703–711 (2021). https://doi.org/10.1007/s10473-021-0304-0

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  • DOI: https://doi.org/10.1007/s10473-021-0304-0

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