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Counting and computing eigenvalues of left-definite Sturm–Liouville problems. (English) Zbl 1019.65056

The paper deals with eigenvalues of left-definite regular self-adjoint Sturm-Liouville problems, with separated or coupled boundary conditions. The authors define a counting function \(N(\lambda)\) which counts the number of positive eigenvalues less than \(\lambda\) when \(\lambda\) is positive and the number of negative eigenvalues greater than \(\lambda\) when \(\lambda\) is negative. Moreover the authors present and describe a code based on this function which allows to numerically compute the eigenvalues. Clear and interesting examples are given to illustrate the use of the code, which is available from one of the authors.

MSC:

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators

Software:

SLEIGN2; LAPACK; aicm
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Full Text: DOI

References:

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