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Dependence of Eigenvalues on the Problem
Author(s) -
Kong Q.,
Wu H.,
Zettl A.
Publication year - 1997
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19971880111
Subject(s) - mathematics , eigenvalues and eigenvectors , monotone polygon , differentiable function , mathematical analysis , boundary value problem , weight function , function (biology) , boundary (topology) , pure mathematics , geometry , physics , quantum mechanics , evolutionary biology , biology
The eigenvalues of linear, regular, two point boundary value problems depend continuously on the problem. In the important self‐adjoint case studied by Naimark and Weidmann this dependence is differentiable and the derivatives of the eigenvalues with respect to a given parameter: an endpoint, a boundary condition, a coefficient, or the weight function, are found. Monotone properties of the eigenvalues with respect to the coefficients and the weight function are established without using the variational (min‐max) characterization.