Journal of Applied Mathematics
Volume 2013 (2013), Article ID 605169, 9 pages
Research Article

Sequential Derivatives of Nonlinear -Difference Equations with Three-Point -Integral Boundary Conditions

Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received 31 October 2012; Accepted 24 January 2013

Academic Editor: Hak-Keung Lam

Copyright © 2013 Nittaya Pongarm 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.


This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinear -difference equations with three-point -integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.