Perturbed functional and neutral functional evolution equations with infinite delay in Frechet spaces

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.

Keywords

• Perturbed functional equation
• neutral evolution equations
• mild solution
• fixed-point theory
• nonlinear alternative
• Frechet spaces
• infinite delay