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Asymptotic properties of solutions to \(n\)-dimensional neutral differential systems. (English) Zbl 1176.34090

Summary: We consider neutral functional differential systems
\[ \begin{aligned} [y_1(t)-a(t)y_1(g(t))]' & =p_1(t)y_2(t),\\ y'_i(t) & = p_i(t)y_{i+1}(t),\quad i=2,3,\dots,n-1,\\ y_n'(t)& = \sigma p_n(t)f(y_1(h(t))),\quad t\geq t_0,\end{aligned} \]
where \(n\geq 3\), \(\sigma=1\) or \(\sigma=-1\).
We find sufficient conditions for solutions either to be oscillatory or to decay to zero. One example is included.

MSC:

34K25 Asymptotic theory of functional-differential equations
34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
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References:

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