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Abstract and Applied Analysis
Volume 2010 (2010), Article ID 236826, 8 pages
Research Article

Positive Solutions for Second-Order Three-Point Eigenvalue Problems

Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu 223300, China

Received 7 June 2010; Accepted 5 August 2010

Academic Editor: Chaitan P. Gupta

Copyright © 2010 Chuanzhi Bai. 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.


With the help of the fixed point index theorem in cones, we get an existence theorem concerning the existence of positive solution for a second-order three-point eigenvalue problem x′′(t)+λf(t,x(t))=0,  0t1,  x(0)=0,  x(1)=x(η), where λ is a parameter. An illustrative example is given to demonstrate the effectiveness of the obtained result.