Abstract and Applied Analysis
Volume 2011 (2011), Article ID 859497, 19 pages
http://dx.doi.org/10.1155/2011/859497
Research Article

Positive Solution of Fourth-Order Integral Boundary Value Problem with Two Parameters

Guoqing Chai

College of Mathematics and Statistics, Hubei Normal University, Hubei 435002, China

Received 12 March 2011; Revised 3 May 2011; Accepted 28 May 2011

Academic Editor: D. Anderson

Copyright © 2011 Guoqing Chai. 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

The author investigates the fourth-order integral boundary value problem with two parameters 𝑢 ( 4 ) ( 𝑡 ) + 𝛽 𝑢 ( 𝑡 ) − 𝛼 𝑢 ( 𝑡 ) = 𝑓 ( 𝑡 , 𝑢 ) , 𝑡 ∈ ( 0 , 1 ) , 𝑢 ( 0 ) = 𝑢 ( 1 ) = 0 , 𝑢 ∫ ( 0 ) = 1 0 𝑢 ( 𝑠 ) 𝜙 1 ( 𝑠 ) 𝑑 𝑠 , 𝑢 ∫ ( 1 ) = 1 0 𝑢 ( 𝑠 ) 𝜙 2 ( 𝑠 ) 𝑑 𝑠 , where nonlinear term function 𝑓 is allowed to change sign. Applying the fixed point index theorem on cone together with the operator spectrum theorem, some results on the existence of positive solution are obtained.