On a class of nonlinear elliptic problems with double phase effects and laplacian-type operators in Musielak-Orlicz-Sobolev spaces

Abstract

This paper addresses the existence of weak solutions for a class of nonlinear Dirichlet boundary value problems governed by a double phase operator. The main results are established under precise assumptions on the nonlinearity of the second term. The analysis is carried out within the advanced framework of Musielak-Orlicz-Sobolev spaces, which accommodate the variable growth conditions induced by the double phase structure. To handle challenges related to weak convergence, we employ the Young measures technique. Additionally, approximate solutions are systematically constructed through the Galerkin method, ensuring a rigorous and structured approach to the problem.