On an abstract nonlinear functional second order Volterra integrodifferential equation

Abstract

In this paper, we prove the existence, uniqueness and boundedness of solutions of a nonlinear functional second order Volterra integrodifferential equation in a general Banach space. The theory of strongly continuous cosine family, modified version of Banach contraction mapping principle and Pachpatte’s integral inequality are main techniques employed in our analysis

Keywords

• volterra integro-differential equations
• cosine family
• modified version of banach contraction mapping principle
• pachpatte's integral inequality