Electron. J. Diff. Equ., Vol. 2011 (2011), No. 101, pp. 1-9.

Oscillation theorems for second-order neutral functional dynamic equations on time scales

Cunchen Gao, Tongxing Li, Shuhong Tang, Ethiraju Thandapani

In this article, we obtain several comparison theorems for the second-order neutral dynamic equation
where $\gamma,\lambda, \beta$ 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
Tongxing Li
School of Control Science and Engineering
Shandong University, Jinan, Shandong 250061, China
email: litongx2007@hotmail.com
Shuhong Tang
School of Information and Control Engineering
Weifang University, Weifang, Shandong 261061, China
email: wfxytang@163.com
Ethiraju Thandapani
Ramanujan Institute for Advanced Study in Mathematics
University of Madras, Chennai, India
email: ethandapani@yahoo.co.in

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