Advances in Difference Equations
Volume 2009 (2009), Article ID 609143, 11 pages
doi:10.1155/2009/609143
Research Article

Existence of Solutions for m-point Boundary Value Problems on a Half-Line

Changlong Yu, Yanping Guo, and Yude Ji

College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, Hebei, China

Received 5 April 2009; Accepted 6 July 2009

Academic Editor: Paul Eloe

Copyright © 2009 Changlong Yu 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

By using the Leray-Schauder continuation theorem, we establish the existence of solutions for m-point boundary value problems on a half-line x″(t)+f(t,x(t),x′(t))=0, 0<t<+∞, x(0)=∑i=1m−2αix(ηi),lim⁡t→+∞x′(t)=0, where αi∈R,∑i=1m−2αi≠1 and 0<η1<η2<⋯<ηm−2<+∞ are given.