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Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential

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Abstract

In this paper, we study the existence and multiplicity of solutions for the Schrödinger–Poisson equations

$$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+\lambda V(x)u+K(x)\phi u=f(x,u)\ \ \ \ \ &{} \ \text{ in }\mathbb {R}^3,\\ -\Delta \phi =K(x)u^2\ \ \ \ \ \ &{} \ \text{ in } \mathbb {R}^3, \end{array}\right. \end{aligned}$$

where \(\lambda >0\) is a parameter, the potential \(V\) may change sign and \(f\) is either superlinear or sublinear in \(u\) as \(|u|\rightarrow \infty \).

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Acknowledgments

The authors express their gratitude to the anonymous referee for a careful reading and helpful suggestions which led to an improvement of the original manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing,  400715, China

    Yiwei Ye & Chun-Lei Tang

  2. Department of Mathematics, Chongqing Normal University, Chongqing,  40133, China

    Yiwei Ye

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  1. Yiwei Ye
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  2. Chun-Lei Tang
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Correspondence to Chun-Lei Tang.

Additional information

Communicated by A. Malchiodi.

Supported by the National Natural Science Foundation of China (No. 11071198).

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Ye, Y., Tang, CL. Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential. Calc. Var. 53, 383–411 (2015). https://doi.org/10.1007/s00526-014-0753-6

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  • DOI: https://doi.org/10.1007/s00526-014-0753-6

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