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Oscillation of third-order neutral differential equations. (English) Zbl 1201.34097

Summary: The objective of this paper is to study asymptotic properties of the couple of third-order neutral differential equations

${\left[a\left(t\right){\left({\left[x\left(t\right)±p\left(t\right)x\left(\delta \left(t\right)\right)\right]}^{\text{'}\text{'}}\right)}^{\gamma }\right]}^{\text{'}}+q\left(t\right){x}^{\gamma }\left(\tau \left(t\right)\right)=0,\phantom{\rule{1.em}{0ex}}t\ge {t}_{0}\phantom{\rule{2.em}{0ex}}\left({\mathrm{E}}^{±}\right)$

where $a\left(t\right),q\left(t\right),p\left(t\right)$ are positive functions, $\gamma >0$ is a quotient of odd positive integers and $\tau \left(t\right)\le t,\delta \left(t\right)\le t$. We will establish some sufficient conditions which ensure that all nonoscillatory solutions of $\left({E}^{±}\right)$ converge to zero. Some examples are considered to illustrate the main results.

##### MSC:
 34K11 Oscillation theory of functional-differential equations
##### References:
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