Boundary Value Problems
Volume 2010 (2010), Article ID 878131, 13 pages
doi:10.1155/2010/878131
Research Article

Existence and Multiplicity of Positive Solutions of a Boundary-Value Problem for Sixth-Order ODE with Three Parameters

Liyuan Zhang and Yukun An

Nanjing University of Aeronautics and Astronautics, 29 Yudao st., Nanjing 210016, China

Received 13 May 2010; Accepted 14 August 2010

Academic Editor: Kanishka Perera

Copyright © 2010 Liyuan Zhang 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

We study the existence and multiplicity of positive solutions of the following boundary-value problem: -u(6)-γu(4)+βu′′-αu=f(t,u), 0<t<1, u(0)=u(1)=u′′(0)=u′′(1)=u(4)(0)=u(4)(1)=0, where f:[0,1]×R+ → R+ is continuous, α, β, and γ∈R satisfy some suitable assumptions.