Abstract
The n-th eigenvalue of a regular Sturm-Liouville problem is not a continuous function of the boundary conditions. On the other hand if the index n is allowed to “jump”, then each eigenvalue can be embedded in an eigenvalue “branch” which is not only continuous but differentiable.
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References
P. B. Bailey, W. N. Everitt and A. Zettl, “Sleign 2” a FORTRAN code for the numerical approximation of eigenvalues, eigenfunctions and continuous spectrum of Sturm-Liouville problems; available through WWW: ftp://ftp.math.niu.edu/pub/papers/Zettl/Sleign2/pub/papers/Zettl/Sleign2
W. N. Everitt, M. Möller and A. Zettl, “Sturm-Liouville problems, discontinuous eigenvalues and the numerical code SLEIGN2”, in preparation.
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© 1997 Springer Basel AG
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Everitt, W.N., Möller, M., Zettl, A. (1997). Discontinuous dependence of the n-th Sturm-Liouville eigenvalue. In: Bandle, C., Everitt, W.N., Losonczi, L., Walter, W. (eds) General Inequalities 7. ISNM International Series of Numerical Mathematics, vol 123. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8942-1_12
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DOI: https://doi.org/10.1007/978-3-0348-8942-1_12
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