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RIGHT-DEFINITE MULTIPARAMETER STURM–LIOUVILLE PROBLEMS WITH EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS

Published online by Cambridge University Press:  14 October 2002

Tirthankar Bhattacharyya ,
Toma$\breve{z}$ Ko$\breve{s}$ir  and
Bor Plestenjak
Tirthankar Bhattacharyya
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India (tirtha@math.iisc.ernet.in)
Toma$\breve{z}$ Ko$\breve{s}$ir
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia (tomaz.kosir@fmf.uni-lj.si; bor.plestenjak@fmf.uni-lj.si)
Bor Plestenjak
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia (tomaz.kosir@fmf.uni-lj.si; bor.plestenjak@fmf.uni-lj.si)
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Abstract

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We study a system of ordinary differential equations linked by parameters and subject to boundary conditions depending on parameters. We assume certain definiteness conditions on the coefficient functions and on the boundary conditions that yield, in the corresponding abstract setting, a right-definite case. We give results on location of the eigenvalues and oscillation of the eigenfunctions.

AMS 2000 Mathematics subject classification: Primary 34B08; 34B24

Keywords

multiparameter Sturm–Liouville boundary-value problemseigenparameter-dependent boundary conditionseigenvaluesoscillation countsMinkowski definiteness conditions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 3 , October 2002 , pp. 565 - 578
Copyright
Copyright © Edinburgh Mathematical Society 2002