The aim of this paper is to extend the result obtained in the author’s previous paper. The problem is related to the Bean critical-state model in type II superconductors with a thermal effect in a multi-connected domain. Mathematically, we are concerned with a coupled system of a quasivariational inequality and a variational equality containing p-curl inequality constraint by a function of a solution of q-Laplacian equality.

quasivariational inequality, stationary coupled system, weak solution.