Boundary Value Problems
Volume 2009 (2009), Article ID 191627, 13 pages
doi:10.1155/2009/191627
Research Article

Existence and Uniqueness of Smooth Positive Solutions to a Class of Singular m-Point Boundary Value Problems

Xinsheng Du and Zengqin Zhao

School of Mathematics Sciences, Qufu Normal University, Qufu, Shandong 273165, China

Received 2 April 2009; Revised 15 September 2009; Accepted 23 November 2009

Academic Editor: Donal O'Regan

Copyright © 2009 Xinsheng Du and Zengqin Zhao. 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 and uniqueness of smooth positive solutions to a class of singular m-point boundary value problems of second-order ordinary differential equations. A necessary and sufficient condition for the existence and uniqueness of smooth positive solutions is given by constructing lower and upper solutions and with the maximal theorem. Our nonlinearity f(t,u,v) may be singular at v,t=0 and/or t=1.