Nonlocal controllability of mild solutions for neutral evolution equations with state-dependent delay in Fréchet spaces

Abstract

In this paper, we prove the controllability of mild solutions of neutral functional evolution equations with state-dependent delay and nonlocal conditions. We establish the non local controllability of mild solutions under certain conditions by combining Avramescu’s nonlinear alternative for the sum of compact and contraction operators in Fréchet spaces with semigroup theory.

Keywords

• neutral evolution equations
• mild solution
• controllability
• infinite delay
• statedependent delay
• nonlocal conditions
• fixed point
• nonlinear alternative
• semigroup theory
• fréchet spaces