Abstract and Applied Analysis
Volume 2012 (2012), Article ID 932019, 17 pages
http://dx.doi.org/10.1155/2012/932019
Research Article

Solvability of Nonlinear Integral Equations of Volterra Type

Zeqing Liu,1 Sunhong Lee,2 and Shin Min Kang2

1Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 2 August 2012; Accepted 23 October 2012

Academic Editor: Kishin B. Sadarangani

Copyright © 2012 Zeqing Liu 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

This paper deals with the existence of continuous bounded solutions for a rather general nonlinear integral equation of Volterra type and discusses also the existence and asymptotic stability of continuous bounded solutions for another nonlinear integral equation of Volterra type. The main tools used in the proofs are some techniques in analysis and the Darbo fixed point theorem via measures of noncompactness. The results obtained in this paper extend and improve essentially some known results in the recent literature. Two nontrivial examples that explain the generalizations and applications of our results are also included.