Positive Solutions To Nonlinear Inclusion Problems In Orlicz-Sobolev Spaces

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.