2003 Decomposition of spectral asymptotics for Sturm-Liouville equations with a turning point
Paul A. Binding, Patrick J. Browne, Bruce A. Watson
Adv. Differential Equations 8(4): 491-511 (2003). DOI: 10.57262/ade/1355926851

Abstract

The Sturm-Liouville equation $-y'' + qy = \lambda ry,$ on $ [0,l],$ is considered subject to the boundary conditions \noindent $y(0)\cos\alpha(0) = y'(0)\sin\alpha(0),$ $y(l)\cos\alpha(l) = y'(l)\sin\alpha(l).$ We assume that $r$ is piecewise continuous with a variety of behaviours at $0, l$ and an interior turning point. We give asymptotic approximations for the eigenvalues $\lambda_n$ of the above boundary value problem in forms equivalent to $\lambda_n = an^2+bn+O(n^\tau)$, where $\tau < 1$.

Citation

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Paul A. Binding. Patrick J. Browne. Bruce A. Watson. "Decomposition of spectral asymptotics for Sturm-Liouville equations with a turning point." Adv. Differential Equations 8 (4) 491 - 511, 2003. https://doi.org/10.57262/ade/1355926851

Information

Published: 2003
First available in Project Euclid: 19 December 2012

zbMATH: 1039.34020
MathSciNet: MR1972598
Digital Object Identifier: 10.57262/ade/1355926851

Subjects:
Primary: 34L20
Secondary: 34B09 , 34B24

Rights: Copyright © 2003 Khayyam Publishing, Inc.

Vol.8 • No. 4 • 2003
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