Electron. J. Differential Equations, Vol. 2021 (2021), No. 14, pp. 1-31.

Existence and concentration results for fractional Schrodinger-Poisson system via penalization method

Zhipeng Yang, Wei Zhang, Fukun Zhao

Abstract:
This article concerns the positive solutions for the fractional Schrodinger-Poisson system

where $\varepsilon>0$ is a small parameter, $(-\Delta)^\alpha$ denotes the fractional Laplacian of orders $\alpha=s,t\in(3/4,1)$, $V\in C(\mathbb{R}^3,\mathbb{R})$ is the potential function and $f:\mathbb{R}\to\mathbb{R}$ is continuous and subcritical. Under a local condition imposed on the potential function, we relate the number of positive solutions with the topology of the set where the potential attains its minimum values. Moreover, we considered some properties of these positive solutions, such as concentration behavior and decay estimate. In the proofs we apply variational methods, penalization techniques and Ljusternik-Schnirelmann theory.

Submitted October 5, 2018. Published March 16, 2021.
Math Subject Classifications: 49J35, 58E05.
Key Words: Penalization method; fractional Schrodinger-Poisson; Lusternik-Schnirelmann theory.
DOI: https://doi.org/10.58997/ejde.2021.14

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Zhipeng Yang
Department of Mathematics
Yunnan Normal University
Kunming 650500, China
email: yangzhipeng326@163.com
Wei Zhang
School of Statistics and Mathematics
Yunnan University of Finance and Economics
Kunming 650221, China
email: weizyn@163.com
Fukun Zhao
Department of Mathematics
Yunnan Normal University
Kunming 650500, China
email: fukunzhao@163.com

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