We consider a quasivariational inequality with a perturbation term and show the existence of a solution to the inequality. The problem is related to the Bean critical-state model in type II superconductors in a multi-connected domain. Mathematically, we are concerned with a quasivariational inequality containing a p-curl inequality with a lower order term constraint by a function of the solution, in a multi-connected domain.

quasivariational inequality, stationary variational problem, existence of solution.