Positive solutions to nonlinear inclusion problems in Orlicz–Sobolev spaces

Abstract

In this paper, we study the existence of positive solutions to a nonlinear elliptic inclusion problem driven by an elliptic differential operator with Dirichlet boundary and a multivalued term depending on the solution and its gradient in reflexive Orlicz–Sobolev spaces by using a linear functional analysis method and a subsolution–supersolution method. We provide some sufficient conditions to ensure that a subsolution and a supersolution exist. An existence theorem for positive solutions of the problem is established.