On the existence of capacity solution for a perturbed thermistor problem in anisotropic Orlicz-Sobolev spaces

In this paper, in the context of anisotropic Orlicz-Sobolev spaces, we analyze the existence of a capacity solution to a system of two coupled perturbed elliptic equations, one of which has a quadratic growth in the gradient and the second one is an non-uniformly elliptic equation. The system describes the heat produced in a semiconductor device by an electric current which may be considered as a generalization of the well-known thermistor problem. We assume that the N-functions do not satisfy the Delta 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _2$$\end{document}-condition.