MULTIVALUED PERTURBATIONS FOR A CLASS OF NONLINEAR EVOLUTION-EQUATIONS

We study in this paper the initial value problem for the multivalued differential equation[Figure not available: see fulltext.] where f is in MS(2) and G is a multifunction from C([0, T];Ω) into the closed subsets of L2(0, Y;Ω), satisfying suitable regularity assumptions. As an application we prove a local existence result for the problem {Mathematical expression}, where G1 (resp. G2) is a lower semicontinuous (resp. upper semicontinuous, convex valued) multifunction from [0, T]×Ω into H. No strong compactness is required for the values of G1 and G2. The differential inclusion (*) is also investigated in the case where G comes from a multivalued regularization of g(t, x, u) and {Mathematical expression}, where g(t, x, u) is a discontinuous real single-valued function defined on [0, T]×Rn×R. © 1991 Fondazione Annali di Matematica Pura ed Applicata.