Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 101, pp. 1-9.
Title: Oscillation theorems for second-order neutral functional dynamic
equations on time scales
Authors: Cunchen Gao (Ocean Univ. of China, Qingdao, China)
Tongxing Li (Shandong Univ., Jinan, China)
Shuhong Tang (Weifang Univ., Shandong, China)
Ethiraju Thandapani (Univ. of Madras, Chennai, India)
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.