Basak Karpuz, Ozkan Ocalan, Radhanath Rath
Abstract:
This article concerns the asymptotic behaviour of solutions to nonlinear
first-order neutral delay dynamic equations involving coefficients
with opposite signs. We present necessary and sufficient conditions for
the solutions to oscillate or to converge to zero.
The coefficient associated with the neutral part is considered in
three distinct ranges, in one of which the coefficient is allowed
to oscillate. Illustrative examples show that the existing results
do not apply to these examples and hence they show the significance
of our results. The results of this article are also new for the
particular choices of the time scale
and
.
Submitted March 10, 2009. Published May 12, 2009.
Math Subject Classifications: 39A10, 39A11.
Key Words: Asymptotic behavior; neutral dynamic equations;
nonoscillation; oscillation; time scale.
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Basak Karpuz Department of Mathematics, Facaulty of Science and arts ANS Campus, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey email: bkarpuz@gmail.com http://www2.aku.edu.tr/~bkarpuz | |
Ozkan Ocalan Department of Mathematics, Faculty of Science and Arts ANS Campus, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey email: ozkan@aku.edu.tr http://www2.aku.edu.tr/~ozkan | |
Radhanath Rath Department of Mathematics Veer Surendra Sai University of Technology Burla, Sambalpur, 768018 Orissa, India email: radhanathmath@yahoo.co.in |
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