## Abstract and Applied Analysis

### Oscillation for Higher Order Dynamic Equations on Time Scales

#### Abstract

We investigate the oscillation of the following higher order dynamic equation: $\{{a}_{n}(t)[({a}_{n-\mathrm{1}}(t)(\cdots ({a}_{\mathrm{1}}(t){x}^{\mathrm{\Delta }}(t){)}^{\mathrm{\Delta }}\cdots {)}^{\mathrm{\Delta }}{)}^{\mathrm{\Delta }}{]}^{\alpha }{\}}^{\mathrm{\Delta }}+p(t){x}^{\beta }(t)=\mathrm{0}$, on some time scale $\mathbf{T}$, where $n\ge \mathrm{2}$, ${a}_{k}(t)$  $\mathrm{}\mathrm{}(\mathrm{1}\le k\le n)$ and $p(t)$ are positive rd-continuous functions on $\mathbf{T}$ and $\alpha ,\beta$ are the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 268721, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393450351

Digital Object Identifier
doi:10.1155/2013/268721

Mathematical Reviews number (MathSciNet)
MR3108669

Zentralblatt MATH identifier
1298.34177

#### Citation

Sun, Taixiang; He, Qiuli; Xi, Hongjian; Yu, Weiyong. Oscillation for Higher Order Dynamic Equations on Time Scales. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 268721, 8 pages. doi:10.1155/2013/268721. https://projecteuclid.org/euclid.aaa/1393450351

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