Interlacing and oscillation for Sturm-Liouville problems with separated and coupled boundary conditions

Authors:
P. A. Binding;H. Volkmer
Affiliations:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alta., Canada;Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI and Department of Mathematics and Statistics, University of Calgary
Venue:
Journal of Computational and Applied Mathematics - Special issue on 60th birthday of Prof. Brian Davies
Year:
2006

Citing 1
Cited 1

Spectral theory of ordinary differential operators

Spectral theory of ordinary differential operators

Relations among eigenvalues of left-definite Sturm-Liouville problems with coupled BCS and separated BCS

Journal of Computational and Applied Mathematics

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Abstract

An extension is given to the known inequalities which interlace the eigenvalues corresponding to separated and coupled boundary conditions for the problem -(py')' + qy = λry on [a, b], assuming 1/p,q and r ∈ L1 ([a, b]). The key is a new interlacing principle for intervals of eigenvalues corresponding to one parameter sets of boundary conditions. Application is given to eigenfunction oscillation.