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Existence of nodal solutions of multi-point boundary value problems

Pages: 457 - 465, Issue Special, September 2009

 Abstract        Full Text (163.3K)              

Lingju Kong - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)
Qingkai Kong - Department of Mathematics, Northern Illinois University, DeKalb, Il 60115, United States (email)

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.

Keywords:  Nodal solutions, multi-point boundary value problems, Sturm-Liouville problems, eigenvalues
Mathematics Subject Classification:  Primary: 34B10; Secondary: 34B15

Received: July 2008;      Revised: March 2009;      Published: September 2009.