International Journal of Differential Equations
Volume 2011 (2011), Article ID 712703, 12 pages
http://dx.doi.org/10.1155/2011/712703
Research Article

On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order

Gao Jia, Li-Na Huang, and Wei Liu

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 4 May 2011; Revised 16 July 2011; Accepted 19 July 2011

Academic Editor: Bashir Ahmad

Copyright © 2011 Gao Jia 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

The estimate of the upper bounds of eigenvalues for a class of systems of ordinary differential equations with higher order is considered by using the calculus theory. Several results about the upper bound inequalities of the ( 𝑛 + 1 )th eigenvalue are obtained by the first 𝑛 eigenvalues. The estimate coefficients do not have any relation to the geometric measure of the domain. This kind of problem is interesting and significant both in theory of systems of differential equations and in applications to mechanics and physics.