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2009, 2009(Special): 269-275. doi: 10.3934/proc.2009.2009.269

Positive solutions to a fourth order three point boundary value problem

John R. Graef 1, , Johnny Henderson 2, and  Bo Yang 3,

1. 

Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States
2. 

Department of Mathematics, Baylor University, Waco, Tx 76798, United States
3. 

Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA 30144

Received  September 2008 Revised  February 2009 Published  September 2009

We consider a three-point boundary value problem for the beam equation. Some a priori estimates to the positive solutions for the boundary value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary value problem are established. The results are illustrated with an example.
Keywords: positive solution, cone, nonlinear boundary-value problem, Fixed point theorem.
Mathematics Subject Classification: Primary: 34B18.
Citation: John R. Graef, Johnny Henderson, Bo Yang. Positive solutions to a fourth order three point boundary value problem. Conference Publications, 2009, 2009 (Special) : 269-275. doi: 10.3934/proc.2009.2009.269
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