Error Estimate of Eigenvalues of Perturbed Higher-Order Discrete Vector Boundary Value Problems

This paper is concerned with the eigenvalues of perturbed higher-order discrete vector boundary value problems. A suitable admissible function space is first introduced, a new variational formula of eigenvalues is then established under certain nonsingularity conditions, and error estimates of eigen...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.611-629-658
Main Authors: Lv, Haiyan, Ren, Guojing, Shi, Yuming
Format: Article
Language:English
Subjects:
Analysis
Boundary value problems
Eigenvalues
Error analysis (Mathematics)
Errors
Estimates
Function space
Mathematical analysis
Mathematics
Perturbation methods
Studies
Vectors (mathematics)
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Summary:This paper is concerned with the eigenvalues of perturbed higher-order discrete vector boundary value problems. A suitable admissible function space is first introduced, a new variational formula of eigenvalues is then established under certain nonsingularity conditions, and error estimates of eigenvalues of problems with small perturbation are finally given by using the variational formula. As a direct consequence, continuous dependence of eigenvalues on boundary value problems is obtained under the nonsingularity conditions. In addition, two special perturbed cases are discussed.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/437506