Nonmonotone, nonlinear evolution inclusions
In this paper, we consider nonlinear evolution problems, defined on an evolution triple of spaces, driven by a nonmonotone operator, and with a perturbation term which is multivalued. We prove existence theorems for the cases of a convex and of a nonconvex valued perturbation term which is defined on all of T x H or only on T x X with values in H or even in X* there X subset of or equal to H subset of or equal to X* is the evolution triple). Also, we prove the existence of extremal solutions, and for the "monotone" problem we have a strong relaxation theorem. Some examples of nonlinear parabolic problems are presented. (C) 2000 Elsevier Science Ltd. All rights reserved.
evolution triple extremal solution parabolic problem pseudomonotone operator l-pseudomonotoncity l-generalized pseudomonotonicity operator of type (s)(+) surjective operator coercive operator compact embedding continuous selection