MILD SOLUTIONS OF NONLINEAR EVOLUTION FUNCTIONAL DIFFERENTIAL INCLUSIONS IN BANACH SPACE

A. Sghir

Abstract

          The existence of a mild solution of the abstract functional differential inclusion

P(φ)

{

u'(t)+Au(t)-F(t,u_{t}) ∋ 0,   t ∈ I = [0,T] u(t)=φ(t),                             t ∈ J = [-r,0]

is obtained by a Filippov technique. Here A is an operator such that A + ωI  is m-accretive for some ω ∈ R⁺, and the multimapping F(t,.) is h(t)-Lipschitzian. The result is applied to a nonlinear functional control problem.