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Zbl 1201.34097
Bacul{\'\i}ková, B.; Džurina, J.
Oscillation of third-order neutral differential equations. (English)
[J] Math. Comput. Modelling 52, No. 1-2, 215-226 (2010). ISSN 0895-7177

Summary: The objective of this paper is to study asymptotic properties of the couple of third-order neutral differential equations $$[a(t)([x(t)\pm p(t)x(\delta(t))]'')^{\gamma}]'+q(t)x^\gamma(\tau(t))=0,\quad t\ge t_0\tag{$E^\pm$}$$ where $a(t), q(t), p(t)$ are positive functions, $\gamma >0$ is a quotient of odd positive integers and $\tau (t)\leq t, \delta (t)\leq t$. We will establish some sufficient conditions which ensure that all nonoscillatory solutions of $(E^{\pm })$ converge to zero. Some examples are considered to illustrate the main results.

MSC 2000:: *34K11 Oscillation theory of functional-differential equations

Keywords: third-order neutral differential equations; oscillation; nonoscillation

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