Existence of nodal solutions of multi-point boundary value problems

Lingju Kong; Qingkai Kong

doi:10.3934/proc.2009.2009.457

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2009, Volume 2009: 457-465. Doi: 10.3934/proc.2009.2009.457 open access

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Existence of nodal solutions of multi-point boundary value problems

Lingju Kong^1, and
Qingkai Kong^2,

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

Received: July 2008

Revised: March 2009

Published: September 2009

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Abstract

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.

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

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