Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces

In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in R. Grimmer, Resolvent operators for integral equations in a Banach space, Transaction of American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions.