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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 $\mathbb{R}^N$.

Strauss and Lions Type Theorems for the Fractional Sobolev Spaces with Variable Exponent and Applications to Nonlocal Kirchhoff–Choquard Problem