## Abstract and Applied Analysis

### Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

#### Abstract

Some oscillation criteria are established for the second-order superlinear neutral differential equations $(r(t)|z'(t){|}^{\alpha -1}z'(t))'+f(t,x(\sigma (t)))=0$, $t\ge {t}_{0}$, where $z(t)=x(t)+p(t)x(\tau (t))$, $\tau (t)\ge t$, $\sigma (t)\ge t$, $p\in C([{t}_{0},\infty ),[0,{p}_{0}])$, and $\alpha \ge 1$. Our results are based on the cases ${\int}_{{t}_{0}}^{\infty}1/{r}^{1/\alpha}(t)\text{d}t=\infty$ or ${\int}_{{t}_{0}}^{\infty}1/{r}^{1/\alpha}(t)\text{d}t\lt \infty$. 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