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Oscillation results for third order nonlinear delay dynamic equations on time scales. (English) Zbl 1235.34242
Summary: We consider the third order nonlinear delay dynamic equations $$(a(t)\{[r(t)x^\Delta(t)]^\Delta+f(t,x(\tau(t)))=0,$$ on a time scale $\bbfT$, where $\gamma>0$ is a quotient of odd positive integers, $a$ and $r$ are positive $rd$-continuous functions on $\bbfT$, and the so-called delay function $\tau:\bbfT\to\bbfT$ satisfies $\tau(t)\le t$, and $\tau(t)\to\infty$ as $t\to\infty$, $f\in C(\bbfT\times\bbfR,\bbfR)$ is assumed to satisfy $uf(t,u)>0$, for $u\ne 0$ and there exists a positive $rd$-continuous function $p$ on $\bbfT$ such that $f(t,u)/u^\gamma\ge p(t)$, for $u\ne 0$. We establish some new results. Some examples are considered to illustrate the main results.

34N05Dynamic equations on time scales or measure chains
34K11Oscillation theory of functional-differential equations
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