Journal of East China Normal University(Natural Sc ›› 2015, Vol. 2015 ›› Issue (3): 9-15.doi: 10.3969/j.issn1000-5641.2015.03.002

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New criteria for oscillation of certain second-order nonlinear dynamic equations on time scales

YANG Jia-shan,HUANG Jin   

  • Received:2014-08-26 Online:2015-05-25 Published:2015-05-28

Abstract: In order to develop and improve the theory about oscillation of dynamic equations on time scales, this paper is concerned with the oscillatory behavior of the following second-order neutral variable delay nonlinear dynamic equation $[A(t)\phi ([x(t)+B(t)g(x(\tau (t)))]^\Delta)]^\Delta +f(t,x(\delta(t)))=0 on a time scale \textbf{T}, where phi (u)=\vert u\vert^{\lambda -1}u$, $\lambda $ is an arbitrary positive constant. By using the calculus theory on time scales and the inequality technique, we establish some new oscillation criteria for the equation. Finally, example is presented to illustrate the effects of our theorems.

Key words: oscillation, time scales, neutral dynamic equations, variable delay, nonlinear neutral term

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