Let n is an element of N, with n >= 2, and let Omega subset of R-n be a bounded domain with smooth boundary partial derivative Omega. Let p is an element of]1, +infinity[, let Y subset of R-n, and let f : Omega x R-h -> R and Psi :Y -> R. be two given functions. We deal with the existence of solutions u = (u(1),..., u(h)) is an element of W-o(l'P) (Omega, R-h) of the implicit equation psi(-Delt