Existence of mild solutions for nonlocal perturbed evolution equations with infinite state-dependent delay in Fréchet spaces

Abstract

In this work, we give sufficient conditions to get the existence of mild solutions for two classes of first-order semilinear functional and neutral functional perturbed evolution equations with infinite state-dependent delay when the conditions are nonlocal using Avramescu nonlinear alternative for the sum of compact operators and contraction maps in Fréchet spaces, combined with semigroup theory.

Keywords

• perturbed evolution equations
• neutral problems
• mild solutions
• state-dependent delay
• fixed point
• nonlinear alternative
• semigroup theory
• fréchet spaces
• infinite delay
• nonlocal conditions