## Abstract and Applied Analysis

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

#### Abstract

We study the following second order mixed nonlinear impulsive differential equations with delay ${(r(t){\Phi }_{\alpha }({x}^{\prime }(t)))}^{\prime }+{p}_{0}(t){\Phi }_{\alpha }(x(t))+{\sum }_{i=1}^{n}{p}_{i}(t){\Phi }_{{\beta }_{i}}(x(t-\sigma ))=e(t),t\ge {t}_{0},t\ne {\tau }_{k},x({\tau }_{k}^{+})={a}_{k}x({\tau }_{k}),x\text{'}({\tau }_{k}^{+})={b}_{k}x\text{'}({\tau }_{k}),k=1,2,\dots$, where ${\Phi }_{*}(u)=|u{|}^{*-1}u$, $\sigma$ is a nonnegative constant, $\{{\tau }_{k}\}$ denotes the impulsive moments sequence, and ${\tau }_{k+1}-{\tau }_{k}>\sigma$. 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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