Electron. J. Differential Equations, Vol. 2022 (2022), No. 47, pp. 1-21.

Multiplicity of high energy solutions for fractional Schrodinger-Poisson systems with critical frequency

Siqi Qu, Xiaoming He

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

where $s\in(1/2,1)$, $\epsilon>0$ is a parameter, $2^*_s=6/(3-2s)$ is the critical Sobolev exponent, $V\in L^{\frac{3}{2s}}(\mathbb{R}^3)$ is a nonnegative function which may be zero in some region of $\mathbb{R}^3$. By means of variational methods, we present the number of high energy bound states with the topology of the zero set of V for small $\epsilon$.

Submitted March 11, 2022. Published July 5, 2022.
Math Subject Classifications: 35B35, 35B40, 35K57, 35Q92, 92C17.
Key Words: Fractional Schrodinger-Poisson system; high energy solution; critical Sobolev exponent.
DOI: https://doi.org/10.58997/ejde.2022.47

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Siqi Qu
College of Science
Minzu University of China
Beijing, 100081, China
email: qusiqi78@gmail.com
Xiaoming He
College of Science
Minzu University of China
Beijing, 100081, China
email: xmhe923@muc.edu.cn

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