Solutions D'une Equation Différantielle Fonctionnelle Semi-Linéaire à Retard Infini Dans Un Espace de Banach

Sghir Abdelhaq

Abstract

        This paper is concerned with the existence of solutions to the initial value problem for a semilinear functional differential equation with infinite delay in a Banach space:

        x'(t) = L xt +f(t,xt)
        t Î [0, a]   (a>0)
        x(t)=φ(t)
        t  Î ]-∞ , 0]


The result is based on the Leray-Schauder alternative and a priori bounds on solutions.