## Journal of Applied Mathematics

### Interval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay

#### Abstract

We study the following second-order super-half-linear impulsive differential equations with delay $[r(t){\phi }_{\gamma }(x\prime (t))]\prime +p(t){\phi }_{\gamma }(x(t-\sigma ))+q(t)f(x(t-\sigma ))=e(t)$, $t\ne {\tau }_{k}$, $x({t}^{+})={a}_{k}x(t),x\prime ({t}^{+})={b}_{k}x\prime (t)$, $t={\tau }_{k}$, where $t\ge {t}_{0}\in {\Bbb R}$, ${\phi }_{{\ast}}(u)=|u{|}^{{\ast}-1}u$, $\sigma$ is a nonnegative constant, $\{{\tau }_{k}\}$ denotes the impulsive moments sequence with ${\tau }_{1}<{\tau }_{2}<\cdots <{\tau }_{k}<\cdots$, ${\mathrm{lim} }_{k\to \infty }{\tau }_{k}=\infty$, and ${\tau }_{k+1}-{\tau }_{k}>\sigma$. By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 285051, 22 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495247

Digital Object Identifier
doi:10.1155/2012/285051

Mathematical Reviews number (MathSciNet)
MR2959988

Zentralblatt MATH identifier
1251.34058

#### Citation

Guo, Zhonghai; Zhou, Xiaoliang; Wang, Wu-Sheng. Interval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay. J. Appl. Math. 2012 (2012), Article ID 285051, 22 pages. doi:10.1155/2012/285051. https://projecteuclid.org/euclid.jam/1355495247