Nonlinear evolution equations on locally closed graphs

Abstract

Let X be a real Banach space, let be an m-dissipative operator, let I a nonempty, bounded interval and let be a given multi-valued function. By using the concept of A-quasi-tangent set introduced by Cârjǎ, Necula, Vrabie [8] and [9] and using a tangency condition expressed in the terms of this concept, we establish a necessary and sufficient condition for C0-viabilityreferringtononlinearevolutioninclusionsoftheformu ′(t) Au(t)+F(t, u(t)),where F is a multi-function defined on the graph of K. As an application, we deduce a comparison result for a class of fully nonlinear evolution inclusions driven by multi-valued perturbations of subdifferentials. © 2010 Real Academia de Ciencias, España.