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Volume 34 • Number 3 • 2011
• Oscillation Results for Third Order Nonlinear Delay Dynamic Equations on Time Scales
Tongxing Li, Zhenlai Han, Shurong Sun and Yige Zhao

In this paper, we consider the third order nonlinear delay dynamic equations $$ (a(t)\{[r(t)x^\Delta(t)]^\Delta\}^\gamma)^\Delta+f(t, x(\tau(t)))=0, $$ on a time scale $\mathbb{T}$, where $\gamma>0$ is a quotient of odd positive integers, $a$ and $r$ are positive $rd$-continuous functions on $\mathbb{T},$ and the so-called delay function $\tau:\mathbb{T}\rightarrow\mathbb{T}$ satisfies $\tau(t)\leq t,$ and $\tau(t)\to\infty$ as $t\to\infty$, $f\in C(\mathbb{T}\times\mathbb{R},\mathbb{R})$ is assumed to satisfy $uf(t,u)>0,$ for $u\neq0$ and there exists a positive $rd$-continuous function $p$ on $\mathbb{T}$ such that $f(t,u)/u^\gamma\geq p(t),$ for $u\neq 0$.
We establish some new results. Some examples are considered to illustrate the main results.

2010 Mathematics Subject Classification: 39A21, 34C10, 34K11, 34N05.

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