[show abstract][hide abstract] ABSTRACT: In this paper sufficient conditions are given ensuring the controllability of mild solutions defined on a bounded interval for two classes of first order semilinear functional and neutral functional differential equations involving evolution operators when the delay is infinite using the nonlinear alternative of Leray-Schauder type.
Surveys in Mathematics and its Applications. 01/2009;
[show abstract][hide abstract] ABSTRACT: This article shows sufficient conditions for the existence of mild solutions, on the positive half-line, for two classes of first-order functional and neutral functional perturbed differential evolution equations with infinite delay. Our main tools are: the nonlinear alternative proved by Avramescu for the sum of contractions and completely continuous maps in Frechet spaces, and the semigroup theory.
Electronic Journal of Differential Equations. 01/2008;