Existence of nodal solutions of multi-point boundary value problems

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2009, 2009(Special): 457-465. doi: 10.3934/proc.2009.2009.457

Existence of nodal solutions of multi-point boundary value problems

1.	Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403
2.	Department of Mathematics, Northern Illinois University, DeKalb, Il 60115, United States

Received July 2008 Revised March 2009 Published September 2009

Abstract
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We study the nonlinear boundary value problem consisting of the equation $y^{''}+ w(t)f(y)=0$ on $[a,b]$ and a multi-point boundary condition. By relating it to the eigenvalues of a linear Sturm-Liouville problem with a two-point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. We also discuss the changes of the existence of different types of nodal solutions as the problem changes.

Keywords: multi-point boundary value problems, Nodal solutions, eigenvalues, Sturm-Liouville problems.

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

Citation: Lingju Kong, Qingkai Kong. Existence of nodal solutions of multi-point boundary value problems. Conference Publications, 2009, 2009 (Special) : 457-465. doi: 10.3934/proc.2009.2009.457

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