## Abstract and Applied Analysis

### Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations

#### Abstract

New oscillation criteria are established for the second-order nonlinear neutralfunctional differential equations of the form ${(r(t){|{z}^{\prime }(t)|}^{\alpha -1}{z}^{\prime }(t))}^{’}+f(t,x[\sigma (t)])=0$, $t\ge {t}_{0}$, where $z(t)=x(t)+p(t)x(\tau (t))$, $p\in {C}^{1}([{t}_{0},\infty ),[0,\infty ))$, and $\alpha \ge 1$. Our results improve andextend some known results in the literature. Some examples are also provided to show theimportance of these results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 819342, 17 pages.

Dates
First available in Project Euclid: 1 April 2013

https://projecteuclid.org/euclid.aaa/1364846436

Digital Object Identifier
doi:10.1155/2012/819342

Mathematical Reviews number (MathSciNet)
MR2947762

Zentralblatt MATH identifier
1251.34083

#### Citation

Sun, Shurong; Li, Tongxing; Han, Zhenlai; Li, Hua. Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 819342, 17 pages. doi:10.1155/2012/819342. https://projecteuclid.org/euclid.aaa/1364846436

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