Dependence of eigenvalues of 2mth-order spectral problems

A regular 2 m th-order spectral problem with self-adjoint boundary conditions is considered in this paper. The continuous dependence of eigenvalues and normalized eigenfunctions on the problem is researched. The derivative formulas of eigenvalues with respect to the given parameters are obtained: en...

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Veröffentlicht in:	Boundary value problems 2017-08, Vol.2017 (1), p.1-35, Article 126
Hauptverfasser:	Zheng, Zhaowen, Ma, Yujuan
Format:	Artikel
Sprache:	eng
Schlagworte:	2mth-order spectral problem Analysis Approximations and Expansions Boundary conditions dependence of eigenvalues on the problem Difference and Functional Equations Eigenvalues Eigenvectors Frechet derivative Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Weighting functions
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Beschreibung
Zusammenfassung:	A regular 2 m th-order spectral problem with self-adjoint boundary conditions is considered in this paper. The continuous dependence of eigenvalues and normalized eigenfunctions on the problem is researched. The derivative formulas of eigenvalues with respect to the given parameters are obtained: endpoints, boundary conditions, coefficients and the weight function. These are of both theoretical and computational importance.
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-017-0857-y