Analytic resolvent semilinear integro‐differential systems: Existence and optimal control

Abstract

The primary contributions of this article are the existence of mild solutions and optimal control for analytic resolvent semilinear integro‐differential systems. Using Lipschitz nonlinearity and the Banach fixed point theorem, we demonstrate results for mild solutions. Using the ‐semigroup, minimizing sequence, Gronwall's inequality, and fundamentals of functional operator theory, we obtain the results for optimal control.