  In this paper we study a class of quasi--variational--hemi\-va\-ria\-tio\-nal
inequalities in reflexive Banach spaces. The inequalities contain a convex
potential, a locally Lipschitz superpotential, and a solution-dependent set of
constraints. Solution existence and compactness of the solution set to the
inequality problem are established based on the Kakutani--Ky Fan--Glicksberg
fixed point theorem. Two examples of the interior and boundary semipermeability
models illustrate the applicability of our results.
