Boundary Value Problems
Volume 2010 (2010), Article ID 874959, 11 pages
doi:10.1155/2010/874959
Research Article

Monotone Positive Solution of Nonlinear Third-Order BVP with Integral Boundary Conditions

Jian-Ping Sun and Hai-Bao Li

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 7 September 2010; Accepted 31 October 2010

Academic Editor: Michel C. Chipot

Copyright © 2010 Jian-Ping Sun and Hai-Bao Li. 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 is concerned with the following third-order boundary value problem with integral boundary conditions 𝑢 ( 𝑡 ) + 𝑓 ( 𝑡 , 𝑢 ( 𝑡 ) , 𝑢 ( 𝑡 ) ) = 0 , 𝑡 ∈ [ 0 , 1 ] ; 𝑢 ( 0 ) = 𝑢 ( 0 ) = 0 , 𝑢 ∫ ( 1 ) = 1 0 𝑔 ( 𝑡 ) 𝑢 ( 𝑡 ) 𝑑 𝑡 , where 𝑓 ∈ 𝐶 ( [ 0 , 1 ] × [ 0 , + ∞ ) × [ 0 , + ∞ ) , [ 0 , + ∞ ) ) and 𝑔 ∈ 𝐶 ( [ 0 , 1 ] , [ 0 , + ∞ ) ) . By using the Guo-Krasnoselskii fixed-point theorem, some sufficient conditions are obtained for the existence and nonexistence of monotone positive solution to the above problem.