Wenbo Wang, Quanqing Li
This article concerns the Schrodinger-Poisson equation
where . We prove that for all , the equation has a ground state solution. The methods used here are based on the Nehari manifold and the concentration-compactness principle. Furthermore, for 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
Kunming, 650500, Yunnan, China
| Quanqing Li |
Department of Mathematics
Mengzi, 661100, Yunnan, China
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