EXISTENCE RESULTS FOR NONDENSELY DEFINED IMPULSIVE SEMILINEAR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY

Mouffak Benchohra (Algérie) and Lech Gòrniewicz (Poland)

Received January 9, 2007

Abstract

In this paper, we investigate the existence of solutions for some classes of semilinear impulsive functional differential inclusions with infinite delay. We assume that the linear part is not necessarily densely defined and satisfies the Hille-Yosida condition on a Banach space X, namely the extrapolated Favard class of the extrapolated semigroup corresponding to the linear part. Our approach is based on the theory of the extrapolation spaces combined with the fixed point theory.

Keywords and phrases: impulsive semilinear functional differential inclusions, mild solution, fixed point, controllability, extrapolation spaces, nondensely defined operator, Hille-Yosida operator.