Systems of differential inclusions with competing operators and variable exponents

Abstract

In this paper, we study a system of differential inclusions with Dirichlet boundary condition, involving competing operators and variable exponents. More precisely, we investigate the existence of both generalized solutions and weak solutions to the problem under consideration. In order to archive our results, we make use of approximation through finite dimensional subspaces via a Galerkin basis along with minimization and nonsmooth analysis.