Journal of Applied Mathematics
Volume 2012 (2012), Article ID 357651, 14 pages
http://dx.doi.org/10.1155/2012/357651
Research Article

First-Order Three-Point Boundary Value Problems at Resonance Part III

Mesliza Mohamed,1 Bevan Thompson,2 and Muhammad Sufian Jusoh3

1Jabatan Matematik dan Statistik, Universiti Teknologi MARA Perlis, 02600 Arau, Malaysia
2Department of Mathematics, The University of Queensland, Brisbane, QLD 4072, Australia
3Fakulti kejuruteraan Awam, Universiti Teknologi MARA Perlis, 02600 Arau, Malaysia

Received 11 December 2011; Accepted 17 January 2012

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 Mesliza Mohamed 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

The main purpose of this paper is to investigate the existence of solutions of BVPs for a very general case in which both the system of ordinary differential equations and the boundary conditions are nonlinear. By employing the implicit function theorem, sufficient conditions for the existence of three-point boundary value problems are established.