On a Nonlocal Problem Involving Fractional P(X, .)-Laplacian with Non-Standard Growth

Abstract

We are concerned in a nonlocal problem involving the fractional p(x, •)−Laplacian operator and with a right-hand side that is a Carathéodory function satisfying only a non-standard growth condition. We show that our problem admits at least one weak solution. In order to do this, the main tool is the Berkovits degree theory for abstract Hammerstein type mappings.