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

doi:10.3969/j.issn1000-5641.2015.03.002

Abstract

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

CLC Number:

O175.7

YANG Jia-shan,HUANG Jin. New criteria for oscillation of certain second-order nonlinear dynamic equations on time scales[J]. Journal of East China Normal University(Natural Sc, 2015, 2015(3): 9-15.

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