Equivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter

Three inverse problems for a Sturm–Liouville boundary value problem − y″+ qy= λy, y(0)cos α= y′(0)sin α and y′(1)= f( λ) y(1) are considered for rational f. It is shown that the Weyl m-function uniquely determines α, f, and q, and is in turn uniquely determined by either two spectra from different v...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2004-03, Vol.291 (1), p.246-261
Main Authors: Binding, Paul A., Browne, Patrick J., Watson, Bruce A.
Format: Article
Language:English
Subjects:
Eigenparameter dependent boundary conditions
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Sciences and techniques of general use
Sturm–Liouville
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Summary:Three inverse problems for a Sturm–Liouville boundary value problem − y″+ qy= λy, y(0)cos α= y′(0)sin α and y′(1)= f( λ) y(1) are considered for rational f. It is shown that the Weyl m-function uniquely determines α, f, and q, and is in turn uniquely determined by either two spectra from different values of α or by the Prüfer angle. For this it is necessary to produce direct results, of independent interest, on asymptotics and oscillation.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2003.11.025