Abstract and Applied Analysis

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

Zhen-Lai Han, Yi-Bing Sun, Yan Zhao, and Dian-Wu Yang

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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 α - 1 z n - 1 t ' + q 0 ( t ) ( x τ 0 t α - 1 x ( τ 0 ( t ) ) + q 1 t ( x ( τ 1 ( t ) ) β - 1 x ( τ 1 ( t ) ) + q 2 t ( x ( τ 2 ( t ) ) γ - 1 x ( τ 2 ( t ) ) = 0 ,   t t 0 , where z ( t ) = x ( t ) + p ( t ) x ( σ ( t ) ) , n is even integer, and γ > α > β > 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

Permanent link to this document
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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