In this work, we study the convergence of a sequence of solutions of degenerate elliptic inclusion problems with variable coercivity and growth exponents. The functional setting involves Lebesgue and Sobolev spaces with variable exponent which varies also with n.

Generalized Lebesgue-Sobolev spaces, Leray-Lions operator, maximal mono- tone graph, bounded Radon diffuse measure, Renormalized solution, electrorheological and Thermorheological fluids, Continuous dependence, Young measures.