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Abstract and Applied Analysis
Volume 2014, Article ID 437506, 19 pages
http://dx.doi.org/10.1155/2014/437506
Research Article

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

1School of Mathematics and Statistics, Anyang Normal University, Anyang, Henan 455000, China
2School of Mathematics, Shandong University, Jinan, Shandong 250100, China
3School of Statistics and Mathematics, Shandong Provincial Key Laboratory of Digital Media Technology, Shandong University of Finance and Economics, Jinan, Shandong 250014, China

Received 23 November 2013; Accepted 30 December 2013; Published 17 February 2014

Academic Editor: Allan Peterson

Copyright © 2014 Haiyan Lv et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.