Electron. J. Differential Equations, Vol. 2020 (2020), No. 47, pp. 1-10.

Positive solutions of Schrodinger-Poisson systems with Hardy potential and indefinite nonlinearity

Yongyi Lan, Biyun Tang, Xian Hu

Abstract:
In this article, we study the nonlinear Schrodinger-Poisson system

where $k\in C(\mathbb{R}^3)$ and 4<p<6, k changes sign in $\mathbb{R}^3$ and $\limsup_{|x|\to\infty}k(x)=k_{\infty}<0$. We prove that Schrodinger-Poisson systems with Hardy potential and indefinite nonlinearity have at least one positive solution, using variational methods.

Submitted April 6, 2020. Published May 21, 2020.
Math Subject Classifications: 35J20, 35J70.
Key Words: Hardy potential; variational methods; indefinite nonlinearity; positive solution.
DOI: 10.58997/ejde.2020.47

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Yongyi Lan
School of Science
Jimei University
Xiamen 61021, China
email: lanyongyi@jmu.edu.cn
Biyun Tang
School of Science
Jimei University
Xiamen 61021, China
email: 1520840642@qq.com
Xian Hu
School of Science
Jimei University
Xiamen 61021, China
email: 2321894958@qq.com

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