Positive solutions to a fourth order three point boundary value problem

John R. Graef; Johnny Henderson; Bo Yang

doi:10.3934/proc.2009.2009.269

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2009, Volume 2009: 269-275. Doi: 10.3934/proc.2009.2009.269 open access

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Positive solutions to a fourth order three point boundary value problem

1.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403
2.
Department of Mathematics, Baylor University, Waco, Tx 76798
3.
Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA 30144

Received: August 31, 2008

Revised: January 31, 2009

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 34B18.

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