On a nonlinear functional second order integrodifferential equation in Banach Spaces

P. M. Dhakanea,* and D. B. Pachpatteb

On a nonlinear functional second order integrodifferential equation in Banach Spaces

Authors :

P. M. Dhakane^a,* and D. B. Pachpatte^b

Author Address :

^aDepartment of Mathematics, S. B. Science College, Aurangabad - 431 001, India.
^bDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431 001, India.

*Corresponding author.

Abstract :

In this paper, we study the existence, uniqueness and other properties of solutions of a nonlinear functional second order Volterra integrodifferential equation in a general Banach space. The techniques used in our analysis are the theory of the strongly continuous cosine family, Schauder fixed point theorem and Pachpatte’s integral inequality.

Keywords :

Integrodifferential equations, Cosine family, Schauder’s fixed point theorem, Pachpatte’s integral inequality.

DOI :

Article Info :

Received : October 16, 2012; Accepted : November 17, 2012.