Oscillation of second order neutral dynamic equations with deviating arguments on time scales

摘要

In this paper, we consider the following second order neutral dynamic equations with deviating arguments on time scales: $$igl(r(t) igl(z^{Delta}(t)igr)^{lpha}igr)^{Delta}+q(t)f igl(yigl(m(t)igr)igr)=0, $$ where (z(t)=y(t)+p(t)y(au(t))), (m(t)leq t) or (m(t)geq t), and (au(t)leq t). Some new oscillatory criteria are obtained by means of the inequality technique and a Riccati transformation. Our results extend and improve many well-known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results.KeywordsTime scales??Oscillation??Neutral??Deviating arguments??MSC26E70??34C10??34K40??1 IntroductionThe study of dynamic equations on time scales which goes back to its founder Hilger [1] as an area of mathematics that has received a lot of attention. It has been created in order to unify the study of differential and difference equations. Many authors have contributed on various aspects of this theory, see the survey paper by Agarwal et al. [2] and the references cited therein.