Local existence for retarded Volterra integrodifferential equations with Hille–Yosida operators

This paper is devoted to finding some existence and uniqueness theorems for classical solutions of the integrodifferential equations with infinite delay. We give some sufficient conditions ensuring the existence and uniqueness of solutions. We assume the linear part is not necessary to be densely defined and satisfies a Hille–Yosida condition so that it is the generator of a nondegenerated, locally Lipschitz continuous integrated semigroup. By using matrix operators and fixed point theorems, we obtain new results for the retarded integrodifferential equations.