Journal of Applied Mathematics
Volume 2011 (2011), Article ID 814103, 40 pages
http://dx.doi.org/10.1155/2011/814103
Research Article

Existence of Solutions for a Class of Variable Exponent Integrodifferential System Boundary Value Problems

Guizhen Zhi,1 Yunrui Guo,2 Yan Wang,1,3 and Qihu Zhang1

1Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China
2Department of Mathematics, Henan Institute of Science and Technology, Xinxiang, Henan 453003, China
3School of Mathematical Science, Xuzhou Normal University, Xuzhou, Jiangsu 221116, China

Received 29 May 2011; Revised 25 September 2011; Accepted 2 October 2011

Academic Editor: Alexandre Carvalho

Copyright © 2011 Guizhen Zhi 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 investigates the existence of solutions for a class of variable exponent integrodifferential system with multipoint and integral boundary value condition in half line. When the nonlinearity term f satisfies sub-(p−−1) growth condition or general growth condition, we give the existence of solutions and nonnegative solutions via Leray-Schauder degree at nonresonance, respectively. Moreover, the existence of solutions for the problem at resonance has been discussed.