Some comments on Sturm-Liouville eigenvalue problems with interior singularities

1987 ◽  
Vol 38 (6) ◽  
pp. 813-838 ◽  
Author(s):  
W. N. Everitt ◽  
J. Gunson ◽  
A. Zettl
Keyword(s):  
Eigenvalue Problems ◽  
Sturm Liouville

Sturm-Liouville eigenvalue problems on time scales

1999 ◽  
Vol 99 (2-3) ◽  
pp. 153-166 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Patricia J.Y. Wong
Keyword(s):  
Time Scales ◽  
Eigenvalue Problems ◽  
Sturm Liouville

scholarly journals Sturm–Liouville Eigenvalue Problems with Finitely Many Singularities

1996 ◽  
Vol 204 (1) ◽  
pp. 74-101 ◽  
Author(s):  
Robert Carlson ◽  
Rod Threadgill ◽  
Carol Shubin
Keyword(s):  
Eigenvalue Problems ◽  
Sturm Liouville

Full- and partial-range eigenfunction expansions for Sturm-Liouville problems with indefinite weights

1984 ◽  
Vol 98 (1-2) ◽  
pp. 69-88 ◽  
Author(s):  
Hans G. Kaper ◽  
Man Kam Kwong ◽  
C. G. Lekkerkerker ◽  
A. Zettl
Keyword(s):  
Hilbert Space ◽  
Differential Expression ◽  
Positive Operator ◽  
Eigenvalue Problems ◽  
Full Range ◽  
Second Order ◽  
Eigenfunction Expansions ◽  
Multiplicative Operator ◽  
Indefinite Weights ◽  
Sturm Liouville

SynopsisThis article is concerned with eigenvalue problems of the form Au = λTu in a Hilbert space H, where Ais a selfadjoint positive operator generated by a second-order Sturm-Liouville differential expression and T a selfadjoint indefinite multiplicative operator which is one-to-one. Emphasis is on the full-range and partial-range expansionproperties of the eigenfunctions.

Inverse Problems in Vibration

1986 ◽  
Vol 39 (7) ◽  
pp. 1013-1018 ◽  
Author(s):  
Graham M. L. Gladwell
Keyword(s):  
Inverse Problems ◽  
Eigenvalue Problems ◽  
Discrete Systems ◽  
Free Vibrations ◽  
Continuous Systems ◽  
Thin Beam ◽  
Inverse Eigenvalue Problems ◽  
Elastic Systems ◽  
Inverse Eigenvalue ◽  
Sturm Liouville

This article concerns infinitesimal free vibrations of undamped elastic systems of finite extent. A review is made of the literature relating to the unique reconstruction of a vibrating system from natural frequency data. The literature is divided into two groups—those papers concerning discrete systems, for which the inverse problems are closely related to matrix inverse eigenvalue problems, and those concerning continuous systems governed either by one or the other of the Sturm–Liouville equations or by the Euler–Bernoulli equation for flexural vibrations of a thin beam.

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