OSCILLATION CRITERIA OF SECOND-ORDER NONLINEAR NEUTRAL FUNCTIONAL DYNAMIC EQUATIONS ON TIME SCALES

S. H. Saker

Abstract


The purpose of this paper is to establish some new sfficient conditions for oscillation of the second-order neutral functional dynamic equation

[ r(t) [y(t)+p(t)y(\tau (t)) ]^{\Delta} ]^{\Delta} + q(t) f(y(\delta(t)))=0,

on a time scale T. The main investigation of the results depends on the generalized Riccati substitution and the analysis of the associated Riccati dynamic inequality. The results improve some oscillation results for neutral dynamic equations in the sense that our results do not require that r^{\delta}(t)>=0 and \int_{t_0}^{\infty} \delta (s) q(s) [1-p(\delta))] \delta_s =\infty.

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ISSN: 1229-1595 (Print), 2466-0973 (Online)