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

Abstract:
In this article, we obtain several comparison theorems for the second-order neutral dynamic equation
$$
 \Big(r(t)\big([x(t)+p(t)x(\tau(t))]^\Delta\big)^\gamma\Big)^\Delta
 +q_1(t)x^\lambda(\delta(t))+q_2(t)x^\beta(\eta(t))=0,
 $$
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.

Show me the PDF file (222 KB), TEX file, and other files for this article.

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

Return to the EJDE web page