Results 201 to 210 of about 147,544 (216)

On the perturbation of eigenvalues for the -Laplacian

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001
Abstract In this Note the differentiability with respect to the domain of the first Dirichlet eigenvalue of the minus p -Laplacian is shown for the first time. An explicit formula for the first variation is obtained. The proof, based on the variational formulation and C 1,α -type estimates, even simplifies the corresponding to the ...
José C. Sabina de Lis, Jorge José García Melián   +1 more
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On Perturbation of Embedded Eigenvalues [PDF]

, 1996
It is well known that in a proper setup eigenvalues which belong to the discrete spectrum are stable. This property is the basis of the perturbation theory for such eigenvalues. On the other hand, the behavior of eigenvalues which are embedded in the continuous spectrum is completely different. Such eigenvalues may be very unstable under perturbations.
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Variational constraints on perturbed eigenvalues and their perturbation expansions

The Journal of Chemical Physics, 1977
The variational principle, in the form of the minimum principle, the Hellmann–Feynman theorem, the curvature theorem, and the virial theorem, is used to derive a number of variational constraints on perturbed exact and variational eigenvalues and on their respective Rayleigh–Schrödinger (RS) and perturbational–variational (PV) perturbation expansions ...
Jeremiah N. Silverman, Jon C. van Leuven
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Eigenvalues of the real generalized eigenvalue equation perturbed by a low-rank perturbation

Journal of Mathematical Chemistry, 1992
The low-rank perturbation (LRP) method solves the perturbed eigenvalue equation (B +V)Ψ k = ɛ k (C +P)Ψ k , where the eigenvalues and the eigenstates of the related unperturbed eigenvalue equationBΦ i = λ i CΦ i are known. The method is designed for arbitraryn-by-n matricesB, V, C, andP, with the only restriction that the eigenstates Φ i of the ...
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Sensitivity of Repeated Eigenvalues to Perturbations

AIAA Journal, 2005
Two methods for calculating the derivatives of a repeated eigenvalue of viscously damped vibrating systems with respect to a parameter are given. The first method implements the subspace spanned by the eigenvectors corresponding to the repeated eigenvalue. The second method is based on an explicit formula that uses the characteristic equation directly,
Su-Seng Pang, Kanika N. Vessel, Yitshak M. Ram   +2 more
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Location and perturbation of eigenvalues

1985
Introduction The eigenvalues of a diagonal matrix are very easy to locate, and the eigenvalues of a matrix are continuous functions of the entries, so it is natural to ask whether one can say anything useful about the eigenvalues of a matrix whose off-diagonal elements are “small” relative to the main diagonal entries.
Roger A. Horn, Charles R. Johnson
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Eigenvalue problems for perturbed p‐Laplacians

AIP Conference Proceedings, 2010
This main subject of this paper is the problem of the existence of eigenvectors and a dispersion analysis of a class of multi parameter eiegen‐value problems for perturbed p‐Laplacians. This paper is particularly, devoted to the problems of describing the eigen‐parameters.
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On the Eigenvalues of a Perturbed Harmonic Oscillator [PDF]

, 1991
We study Schrodinger operators on Rn of the form $$H = {H_v} = - \Delta + q(x) + V(x) $$ where q(x) is a positive definite quadratic form and V(x) a potential which may be considered as a perturbation. We show that the discrete spectrum of H has similar properties as that of the unperturbed H0 = -∆+q.
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Eigenvalue reanalysis by improved perturbation

International Journal for Numerical Methods in Engineering, 1988
AbstractA new efficient method of eigenvalue reanalysis has been developed based on the perturbation method such that first the differential equations which describe the change of the eigenvalues and eigenvectors of a system being modified are derived from the perturbation method and then the solutions of these equations are obtained by following them ...
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Singularly Perturbed Eigenvalue Problems

SIAM Journal on Applied Mathematics, 1987
This paper is concerned with eigenvalue problems of singularly perturbed linear ordinary differential equations. A common way to treat such problems is to derive an approximating eigenvalue problem by the use of matched asymptotic expansions.It is shown that under appropriate assumptions a domain in the complex plane can be identified, in which the ...
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