Nonlinear functional integrodifferential equations in Hilbert space

Abstract

Let X be a Hilbert space and let Ω⊂Rn be a bounded domain with smooth boundary ∂Ω. We establish the existence and norm estimation of solutions for the parabolic partial functional integro-differential equation in X by using the fundamental solution.

Keywords

• Functional integro-differential equation
• elliptic differential operators
• fundamental solution
• Gårding's inequality
• successive approximation
• norm estimation.