OSCILLATION OF NONLINEAR SECOND ORDER NEUTRAL DELAY DYNAMIC EQUATIONS ON TIME SCALES

Title & Authors
OSCILLATION OF NONLINEAR SECOND ORDER NEUTRAL DELAY DYNAMIC EQUATIONS ON TIME SCALES
Agwo, Hassan A.;

Abstract
In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $\small{(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0}$ on a time scale $\small{{\mathbb{T}}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when $\small{{\mathbb{T}}={\mathbb{R}}}$, neutral delay difference equations when $\small{{\mathbb{T}}={\mathbb{N}}}$ and for neutral delay q-difference equations when $\small{{\mathbb{T}}=q^{\mathbb{N}}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.
Keywords
oscillation;time scales;neutral delay;dynamic equation;
Language
English
Cited by
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6.
Oscillatory Behavior of Quasilinear Neutral Delay Dynamic Equations on Time Scales, Advances in Difference Equations, 2010, 2010, 1
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