Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 47, pp. 1-21.

Title: Multiplicity of high energy solutions for fractional  Schrodinger-Poisson systems with critical frequency
       
Authors: Siqi Qu     (Minzu Univ. of China, Beijing, China)
         Xiaoming He (Minzu Univ. of China, Beijing, China)

Abstract: 
In this article we study the fractional Schrodinger-Poisson system
$$\displaylines{
 \epsilon^{2s}(-\Delta)^s u+V(x)u=\phi |u|^{2^*_s-3}u,\quad x\in \mathbb{R}^3, \cr
 (-\Delta)^s\phi=|u|^{2^*_s-1}, \quad x\in \mathbb{R}^3,
}$$
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 05, 2022.
Math Subject Classifications: 35B35, 35B40, 35K57, 35Q92, 92C17.
Key Words: Fractional Schrodinger-Poisson system; high energy solution; critical Sobolev exponent.