Abstract and Applied Analysis

Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

Tongxing Li, Zhenlai Han, Chenghui Zhang, and Hua Li

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Abstract

Some oscillation criteria are established for the second-order superlinear neutral differential equations ( r ( t ) | z ' ( t ) | α - 1 z ' ( t ) ) ' + f ( t , x ( σ ( t ) ) ) = 0 , t t 0 , where z ( t ) = x ( t ) + p ( t ) x ( τ ( t ) ) , τ ( t ) t , σ ( t ) t , p C ( [ t 0 , ) , [ 0 , p 0 ] ) , and α 1 . Our results are based on the cases t 0 1 / r 1 / α ( t ) d t = or t 0 1 / r 1 / α ( t ) d t < . Two examples are also provided to illustrate these results.

Article information

Source
Abstr. Appl. Anal., Volume 2011, Number 1 (2011), Article ID 367541, 17 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171396

Digital Object Identifier
doi:10.1155/2011/367541

Mathematical Reviews number (MathSciNet)
MR2776752

Zentralblatt MATH identifier
1217.34112

Citation

Li, Tongxing; Han, Zhenlai; Zhang, Chenghui; Li, Hua. Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations. Abstr. Appl. Anal. 2011 (2011), no. 1, Article ID 367541, 17 pages. doi:10.1155/2011/367541. https://projecteuclid.org/euclid.aaa/1313171396


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