Abstract and Applied Analysis

Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

Zhonghai Guo, Xiaoliang Zhou, and Wu-Sheng Wang

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Abstract

We study the following second order mixed nonlinear impulsive differential equations with delay ( r ( t ) Φ α ( x ( t ) ) ) + p 0 ( t ) Φ α ( x ( t ) ) + i = 1 n p i ( t ) Φ β i ( x ( t - σ ) ) = e ( t ) , t t 0 , t τ k , x ( τ k + ) = a k x ( τ k ) , x ' ( τ k + ) = b k x ' ( τ k ) , k = 1,2 , , where Φ * ( u ) = | u | * - 1 u , σ is a nonnegative constant, { τ k } denotes the impulsive moments sequence, and τ k + 1 - τ k > σ . Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 351709, 23 pages.

Dates
First available in Project Euclid: 1 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364846443

Digital Object Identifier
doi:10.1155/2012/351709

Mathematical Reviews number (MathSciNet)
MR2935142

Zentralblatt MATH identifier
1245.34070

Citation

Guo, Zhonghai; Zhou, Xiaoliang; Wang, Wu-Sheng. Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 351709, 23 pages. doi:10.1155/2012/351709. https://projecteuclid.org/euclid.aaa/1364846443


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