PARAMETRIC ROBIN DOUBLE PHASE PROBLEMS WITH CRITICAL GROWTH ON THE BOUNDARY

Abstract

The aim of this paper is to study a double phase problem with nonlinear boundary condition of critical growth and with a superlinear righthand side that does not satisfy the Ambrosetti-Rabinowitz condition. Based on an equivalent norm in the Musielak-Orlicz Sobolev space along with variational tools and critical point theory, we prove the existence of at least two nontrivial, bounded weak solutions.