Oscillatory Behavior of Quasilinear Neutral Delay Dynamic Equations on Time Scales

• Main Authors: Zhang Chenghui, Han Zhenlai, Sun Shurong, Li Tongxing
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Advances in Difference Equations
• Online Access: http://www.advancesindifferenceequations.com/content/2010/450264

<p/> <p>By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations <inline-formula><graphic file="1687-1847-2010-450264-i1.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-450264-i2.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2010-450264-i3.gif"/></inline-formula>, and the time scale interval is <inline-formula><graphic file="1687-1847-2010-450264-i4.gif"/></inline-formula>. Our results in this paper not only extend the results given by Agarwal et al. (2005) but also unify the oscillation of the second-order neutral delay differential equations and the second-order neutral delay difference equations.</p>