American Institute of Mathematical Sciences

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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

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, United States

Received  July 2008 Revised  March 2009 Published  September 2009

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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