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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
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