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

John R. Graef; Lingju Kong

doi:10.3934/proc.2011.2011.515

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2011, Volume 2011: 515-522. Doi: 10.3934/proc.2011.2011.515 open access

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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

Received: June 2010

Revised: April 2011

Published: August 2017

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Abstract

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].

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Mathematics Subject Classification: Primary: 34B15; Secondary: 34B10, 34B18.

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