Cunchen Gao, Tongxing Li, Shuhong Tang, Ethiraju Thandapani
Abstract:
In this article, we obtain several comparison theorems for the
second-order neutral dynamic equation
![$$
\Big(r(t)\big([x(t)+p(t)x(\tau(t))]^\Delta\big)^\gamma\Big)^\Delta
+q_1(t)x^\lambda(\delta(t))+q_2(t)x^\beta(\eta(t))=0,
$$](gifs/aa.gif)
where
are ratios of positive
odd integers. We compare such equation with the first-order
dynamic inequalities in the sense that the absence of the
eventually positive solutions of these first-order inequalities
implies the oscillation of the studied equation.
Submitted March 21, 2011. Published August 10, 2011.
Math Subject Classifications: 34K11, 39A21, 34N05.
Key Words: Oscillation; neutral functional dynamic equation;
comparison theorem; time scales.
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Cunchen Gao College of Information Science and Engineering Ocean University of China, Qingdao, Shandong 266100, China email: ccgao@ouc.edu.cn |
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Tongxing Li School of Control Science and Engineering Shandong University, Jinan, Shandong 250061, China email: litongx2007@hotmail.com |
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Shuhong Tang School of Information and Control Engineering Weifang University, Weifang, Shandong 261061, China email: wfxytang@163.com |
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Ethiraju Thandapani Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chennai, India email: ethandapani@yahoo.co.in |
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