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Oscillation criteria of Hille and Nehari types for third-order delay differential equations. (English) Zbl 1139.34049
Summary: The objective of this paper is to systematically study oscillation and asymptotic behavior of the third order-nonlinear delay differential equation
$((x''(t))\gamma)'+q(t)x''(\tau(t))=0, \quad t\geq t_0,$
where $$q(t)$$ is a positive function, $$\gamma> 0$$ is a quotient of odd positive integers, and the delay function $$\tau(t)\leq t$$ satisfies $$\lim_{t\to\infty}\tau(t)=\infty$$. We establish some sufficient conditions of Hille and Nehari types, which ensure that (*) is oscillatory or the solutions converge to zero.

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