## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2011 (2011), Article ID 712703, 12 pages.

### 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

#### 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.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2011 (2011), Article ID 712703, 12 pages.

**Dates**

Received: 4 May 2011

Revised: 16 July 2011

Accepted: 19 July 2011

First available in Project Euclid: 25 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1485313234

**Digital Object Identifier**

doi:10.1155/2011/712703

**Mathematical Reviews number (MathSciNet)**

MR2832511

**Zentralblatt MATH identifier**

1239.34021

#### Citation

Jia, Gao; Huang, Li-Na; Liu, Wei. On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order. Int. J. Differ. Equ. 2011 (2011), Article ID 712703, 12 pages. doi:10.1155/2011/712703. https://projecteuclid.org/euclid.ijde/1485313234