Mild Solution and Approximate Controllability of Retarded Semilinear Systems with Control Delays and Nonlocal Conditions

Abstract

This work studies the approximate controllability of a class of first-order retarded semilinear differential equations with delays in control and nonlocal conditions. First we deduce the existence of mild solutions using fixed point approach. For this, the nonlinear function is supposed to be locally Lipschitz, which is a weaker condition than Lipschitz continuity. Controllability results of the system are shown by using the approximate and iterative technique. The results are illustrated by providing an example.

Keywords:

• Approximate controllability
• fixed point
• mild solution
• strongly continuous semigroup