Positive solutions of a nonlinear higher order boundary-value problem

John R. Graef; Lingju Kong; Bo Yang

doi:10.3934/proc.2009.2009.276

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2009, Volume 2009: 276-285. Doi: 10.3934/proc.2009.2009.276 open access

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Positive solutions of a nonlinear higher order boundary-value problem

1.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403
2.
Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA 30144

Received: June 30, 2008

Revised: March 31, 2009

Published: August 2009

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Abstract

The authors study a higher order three point boundary value problem. Estimates for positive solutions are given; these estimates improve some recent results in the literature. Using these estimates, new sufficient conditions for the existence and nonexistence of positive solutions of the problem are obtained. An example illustrating the results is included.

Keywords:

Existence and nonexistence of positive solutions; Guo-Krasnosel'skii fixed point theorem; higher order boundary value problem.

Mathematics Subject Classification: Primary: 34B18 Secondary: 53C35.

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