Kirchhoff type elliptic equations with double criticality in Musielak–Sobolev spaces

Abstract

This paper aims to establish the existence of a weak solution for the nonlocal problem: where is a bounded and smooth domain containing two open and connected subsets and such that and is the -Laplace operator. We assume that reduces to in and to in , the nonlinear function acts as on and as on for sufficiently large . To establish the existence results in a Musielak–Sobolev space, we use a variational technique based on the mountain pass theorem.