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http://dx.doi.org/10.4134/BKMS.2008.45.2.299

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

Agwo, Hassan A. (Department of Mathematics Ain Shams University Aculty of Education)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 299-312 More about this Journal
Abstract
In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. 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 ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ 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;
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Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 5
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