Nonhomogeneous multiparameter problems in Orlicz–Sobolev spaces

Abstract

This paper is concerned with the existence and multiplicity of solutions for a class of problems involving the Φ‐Laplacian operator with general assumptions on the nonlinearities, which include both semipositone cases and critical concave convex problems. The research is based on the subsupersolution technique combined with a truncation argument and an application of the Mountain Pass Theorem. The results in this paper improve and complement some recent contributions to this field.