International Journal of Differential Equations
Volume 2011 (2011), Article ID 376753, 11 pages
http://dx.doi.org/10.1155/2011/376753
Research Article

Existence of Positive Solutions for Neumann Boundary Value Problem with a Variable Coefficient

Dongming Yan,1 Qiang Zhang,2 and Zhigang Pan1

1Department of Mathematics, Sichuan University, Chengdu, China
2School of Computer Science, Civil Aviation Flight University of China, Guanghan, China

Received 25 May 2011; Accepted 27 July 2011

Academic Editor: Bashir Ahmad

Copyright © 2011 Dongming Yan 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

We consider the existence of positive solutions for the Neumann boundary value problem 𝑥 ( 𝑡 ) + 𝑚 2 ( 𝑡 ) 𝑥 ( 𝑡 ) = 𝑓 ( 𝑡 , 𝑥 ( 𝑡 ) ) + 𝑒 ( 𝑡 ) , 𝑡 ∈ ( 0 , 1 ) , 𝑥 ( 0 ) = 0 , 𝑥 ( 1 ) = 0 , where 𝑚 ∈ 𝐶 ( [ 0 , 1 ] , ( 0 , + ∞ ) ) , 𝑒 ∈ 𝐶 [ 0 , 1 ] , and 𝑓 ∶ [ 0 , 1 ] × ( 0 , + ∞ ) → [ 0 , + ∞ ) is continuous. The theorem obtained is very general and complements previous known results.