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 \(\Delta _2\) ${\mathrm{\Delta }}_2$ -condition.