Solvability of nondensely defined partial functional integrodifferential equations using the integrated resolvent operators

Abstract

In this work, we study the existence and regularity of solutions for a class of nondensely defined partial functional integrodifferential equations. We suppose that the undelayed part admits an integrated resolvent operator in the sense given by Oka [J. Integral Equations Appl. 7(1995), 193–232.]. We give some sufficient conditions ensuring the existence, uniqueness and regularity of solutions. The continuous dependence on the initial data of solutions is also proved. Some examples are provided to illustrate our abstract theory.

Keywords

• partial functional integrodifferential equations
• integrated semigroup
• integrated resolvent operator
• integral solution
• strict solution