Electron. J. Differential Equations, Vol. 2020 (2020), No. 01, pp. 1-17.

Fractional Schrodinger-Poisson systems with weighted Hardy potential and critical exponent

Yu Su, Haibo Chen, Senli Liu, Xianwen Fang

Abstract:
In this article we consider the fractional Schrodinger-Poisson system

where $s\in(0,3/4)$, $t\in(0,1)$, $2t+4s=3$, $\lambda>0$ and $2^*_s=6/(3-2s)$ is the Sobolev critical exponent. By using perturbation method, we establish the existence of a solution for $\lambda$ small enough.

Submitted October 24, 2019. Published January 6, 2020.
Math Subject Classifications: 35B38, 35J47.
Key Words: Fractional Schrodinger-Poisson system; weighted Hardy potential; critical exponent.
DOI: 10.58997/ejde.2020.01

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Yu Su
School of Mathematics and Big Data
Anhui University of Science and Technology
Huainan, 232001 Anhui, China
email: yusumath@qq.com
Haibo Chen
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: math_chb@163.com
Senli Liu
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: jasonliu0615@163.com
Xianwen Fang
School of Mathematics and Big Data
Anhui University of Science and Technology
Huainan, 232001 Anhui, China
email: xwfang@aust.edu.cn

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