Existence of a weak solution for nonlocal thermistor problem in Sobolev spaces with variable exponent

Abstract

The focus of this paper is to establish the existence of a weak solution for a problem that involves p(x)-Laplacian. We achieve this by utilizing the topological degree theory, which is based on a class of demi-continuous operators of generalized (S+) type, as presented in [5], in conjunction with the theory of variable-exponent Sobolev spaces. Additionally, we provide a numerical example to verify and validate the theoretical results.