Doubly coupled systems of elliptic hemivariational inequalities: Existence and location

Abstract

We develop an approach based on the subsolution–supersolution method for an elliptic system of hemivariational inequalities. The system exhibits full dependence on the gradient of the solution and is doubly coupled on both the source and multivalued terms. We prove the existence of solutions in a prescribed trapping region and, as an application, provide a criterion for obtaining positive solutions.