Three solutions for fractional $p(x,.)$-Laplacian Dirichlet problems with weight

Abstract

The aim of this paper is to investigate weak solutions for a problem involving the fractional p(x, .)-Laplacian operator with weight. The main tool used for obtaining the existence result is a recent three critical-points theorem established by Ricceri. Moreover, we establish some new continuous and compact embedding theorems of the fractional Sobolev spaces with variable exponent into the Hölder spaces.