On Forced Periodic Solutions of Superlinear Quasi-parabolic Problems

Abstract

We study the existence of periodic solutions for a class of quasi-parabolic equations involving the p-Laplacian (or any other nonlinear operators of similar class) perturbed by nonlinear terms and forced by rather irregular periodic in time excitations (including what we call abrupt changes). These equations may model problems for which, aside from the presence of the kind of nonlinear dissipation associated to the p-Laplacian, other nonlinear and not necessarily dissipative mechanisms occur. We look for boundedness conditions on these periodic excitations and nonlinear perturbations sufficient to guarantee the existence of periodic responses (solutions) of the same period.