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2011, 2011(Special): 515-522. doi: 10.3934/proc.2011.2011.515

Uniqueness and parameter dependence of positive solutions of third order boundary value problems with $p$-laplacian

John R. Graef 1, and  Lingju Kong 1,

1. 

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

Received  June 2010 Revised  April 2011 Published  October 2011

We consider the boundary value problem with nonhomogeneous three-point boundary condition Sufficient conditions are obtained for the existence and uniqueness of a positive solution. The dependence of the solution on the parameter $\lambda$ is also studied. This work extends and improves some recent results in the literature on the above problem, especially those in the paper [L. Kong, D. Piao, and L. Wang, Positive solutions for third order boundary value problems with $p$-Laplacian, Result. Math. 55 (2009) 111{128].
Keywords: boundary value problems, Positive solutions, uniqueness, dependence on a parameter.
Mathematics Subject Classification: Primary: 34B15; Secondary: 34B10, 34B18.
Citation: John R. Graef, Lingju Kong. Uniqueness and parameter dependence of positive solutions of third order boundary value problems with $p$-laplacian. Conference Publications, 2011, 2011 (Special) : 515-522. doi: 10.3934/proc.2011.2011.515
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