## Abstract and Applied Analysis

### Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations with Mixed Nonlinearities

#### Abstract

We establish some oscillation criteria for the following certain even order neutral delay differential equations with mixed nonlinearities: ${(r(t){|{z}^{(n-1)}(t)|}^{\alpha -1}{z}^{(n-1)}(t))}^{\text{'}}+{q}_{0}(t){|(x({\tau }_{0}(t))|}^{\alpha -1}x({\tau }_{0}(t))+{q}_{1}(t){|(x({\tau }_{1}(t))|}^{\beta -1}x({\tau }_{1}(t))+{q}_{2}(t){|(x({\tau }_{2}(t))|}^{\gamma -1}x({\tau }_{2}(t))=0,\mathrm{ }t\ge {t}_{0},$ where $z(t)=x(t)+p(t)x(\sigma (t)),$ $n$ is even integer, and $\gamma >\alpha >\beta >0.$ Our results generalize and improve some known results for oscillation of certain even order neutral delay differential equations with mixed nonlinearities.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 629074, 11 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425049074

Digital Object Identifier
doi:10.1155/2014/629074

Mathematical Reviews number (MathSciNet)
MR3248866

Zentralblatt MATH identifier
07022769

#### Citation

Han, Zhen-Lai; Sun, Yi-Bing; Zhao, Yan; Yang, Dian-Wu. Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations with Mixed Nonlinearities. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 629074, 11 pages. doi:10.1155/2014/629074. https://projecteuclid.org/euclid.aaa/1425049074

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