American Institute of Mathematical Sciences

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2009, 2009(Special): 276-285. doi: 10.3934/proc.2009.2009.276

Positive solutions of a nonlinear higher order boundary-value problem

John R. Graef 1, , Lingju Kong 1, and  Bo Yang 2,

1. 

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

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

Received  July 2008 Revised  April 2009 Published  September 2009

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.
Citation: John R. Graef, Lingju Kong, Bo Yang. Positive solutions of a nonlinear higher order boundary-value problem. Conference Publications, 2009, 2009 (Special) : 276-285. doi: 10.3934/proc.2009.2009.276
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