The authors study the following class of functional-differential equations with infinite delay in a Banach space
where is a closed linear operator. Existence, uniqueness and regularity results for the same class of equations were previously furnished by H. R. Henríquez [Funkc. Ekvacioj, Ser. Int. 37, No. 2, 329–343 (1994; Zbl 0814.35141); Indian J. Pure Appl. Math. 27, No. 4, 357–386 (1996; Zbl 0853.34072) and Nonlinear Anal., Theory Methods Appl. 28, No. 3, 513–531 (1997; Zbl 0864.35112)] in the case where is an infinitesimal generator of a -semigroup on .
The aim of the present paper is to extend such existence results to the case where is a Hille-Yosida operator with domain not necessarily dense in . The theory of integrated semigroups is the main tool used. The authors apply the result to a partial integrodifferential equation.