Boundary Value Problems
Volume 2009 (2009), Article ID 362983, 16 pages
doi:10.1155/2009/362983
Research Article

Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems

Minghe Pei1 and Sung Kag Chang2

1Department of Mathematics, Bei Hua University, JiLin 132013, China
2Department of Mathematics, Yeungnam University, Kyongsan 712-749, South Korea

Received 5 February 2009; Accepted 14 July 2009

Academic Editor: Kanishka Perera

Copyright © 2009 Minghe Pei and Sung Kag Chang. 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 are concerned with the higher-order nonlinear three-point boundary value problems: x(n)=f(t,x,x′,…,x(n−1)),n≥3, with the three point boundary conditions g(x(a),x′(a),…,x(n−1)(a))=0; x(i)(b)=μi,i=0,1,…,n−3;h(x(c),x′(c),…,x(n−1)(c))=0, where a<b<c,f:[a,c]×ℝn→ℝ=(−∞,+∞) is continuous, g,h:ℝn→ℝ are continuous, and μi∈ℝ,i=0,1,…,n−3 are arbitrary given constants. The existence and uniqueness results are obtained by using the method of upper and lower solutions together with Leray-Schauder degree theory. We give two examples to demonstrate our result.