Strauss and Lions type theorems for the fractional Sobolev spaces with variable exponent and applications to nonlocal Kirchhoff-Choquard problem

Abstract

This paper deals with Strauss and Lions-type theorems for fractional Sobolev spaces with variable exponent $W^{s,p(.),\tilde{p}(.,.)}(\Omega )$, when $p$ and $\tilde{p}$ satisfies some conditions. As application, we study the existence of solutions for a class of Kirchhoff-Choquard problem in ${\mathbb{R}}^N$.