Electron. J. Diff. Equ., Vol. 2011 (2011), No. 31, pp. 1-10.

Existence and uniqueness of solutions of nonlinear mixed integrodifferential equations with nonlocal condition in Banach Spaces

Machindra B. Dhakne, Haribhau L. Tidke

In this article, we study the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition in Banach spaces. Furthermore, we study continuous dependence of mild solutions. Our analysis is based on semigroup theory and Banach fixed point theorem.

Submitted April 28, 2010. Published February 18, 2011.
Math Subject Classifications: 45N05, 47B38, 47H10.
Key Words: Existence and uniqueness; mild and strong solutions; mixed Volterra-Fredholm; integrodifferential equation; Banach fixed point theorem; nonlocal condition.

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Machindra B. Dhakne
Department of Mathematics
Dr. Babasaheb Ambedkar Marathwada University
Aurangabad-431 004, India
email: mbdhakne@yahoo.com
Haribhau L. Tidke
Department of Mathematics, School of Mathematical Sciences
North Maharashtra University
Jalgaon-425 001, India
email: tharibhau@gmail.com

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