EXISTENCE RESULTS FOR IMPULSIVE PERTURBED PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS IN FRECHET SPACES

摘要

In this paper, we prove the existence of mild solutions for first-order impulsive neutral functional perturbed differential equations with infinite delay. Our main tools are the recently found nonlinear alternative by Avramescu for the sum of contractions and completely continuous maps in Frechet spaces and the semi-group theory. Also we claim that the phase space considered by several authors is not correct and we give a new definition of the phase space. An example is given to illustrate the theory.