Electron. J. Differential Equations, Vol. 2020 (2020), No. 78, pp. 1-19.

Existence and concentration of positive ground states for Schrodinger-Poisson equations with competing potential functions

Wenbo Wang, Quanqing Li

This article concerns the Schrodinger-Poisson equation

where $3<q<p<5=2^{\ast}-1$. We prove that for all $\varepsilon>0$, the equation has a ground state solution. The methods used here are based on the Nehari manifold and the concentration-compactness principle. Furthermore, for $\varepsilon>0$ small, these ground states concentrate at a global minimum point of the least energy function.

Submitted January 11, 2019. Published July 22, 2020.
Math Subject Classifications: 35J15, 35J20, 35J50.
Key Words: Schrodinger-Poisson equation; Nehari manifold; ground states; concentration-compactness; concentration.

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Wenbo Wang
School of Mathematics and Statistics
Yunnan University
Kunming, 650500, Yunnan, China
email: wenbowangmath@163.com
Quanqing Li
Department of Mathematics
Honghe University
Mengzi, 661100, Yunnan, China
email: shili06171987@126.com

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