Abstract and Applied Analysis
Volume 2011 (2011), Article ID 714728, 13 pages
http://dx.doi.org/10.1155/2011/714728
Research Article

Positive Solutions for Singular Complementary Lidstone Boundary Value Problems

Fanglei Wang1 and Yukun An2

1College of Science, Hohai University, Nanjing 210098, China
2Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 11 June 2011; Accepted 6 November 2011

Academic Editor: Gaston Mandata N'Guerekata

Copyright © 2011 Fanglei Wang and Yukun An. 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 fixed-point theorems of a cone, we investigate the existence and multiplicity of positive solutions for complementary Lidstone boundary value problems: ( − 1 ) 𝑛 𝑢 ( 2 𝑛 + 1 ) ( 𝑡 ) = ℎ ( 𝑡 ) 𝑓 ( 𝑢 ( 𝑡 ) ) , in 0 < 𝑡 < 1 , 𝑢 ( 0 ) = 0 , 𝑢 ( 2 𝑖 + 1 ) ( 0 ) = 𝑢 ( 2 𝑖 + 1 ) ( 1 ) = 0 , 0 ≤ 𝑖 ≤ 𝑛 − 1 , where 𝑛 ∈ 𝑁 .