Abstract and Applied Analysis
Volume 2012 (2012), Article ID 137576, 26 pages
http://dx.doi.org/10.1155/2012/137576
Research Article

On Semilinear Integro-Differential Equations with Nonlocal Conditions in Banach Spaces

Tran Dinh Ke,1 Valeri Obukhovskii,2 Ngai-Ching Wong,3 and Jen-Chih Yao4

1Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi 10307, Vietnam
2Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043 Voronezh, Russia
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
4Center for General Education, Kaohsiung Medical University, Kaohsiung 80702, Taiwan

Received 13 November 2011; Accepted 11 January 2012

Academic Editor: Malisa R. Zizovic

Copyright © 2012 Tran Dinh Ke et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the abstract Cauchy problem for a class of integrodifferential equations in a Banach space with nonlinear perturbations and nonlocal conditions. By using MNC estimates, the existence and continuous dependence results are proved. Under some additional assumptions, we study the topological structure of the solution set.