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Graef, John R.; Spikes, Paul W.

On the oscillation of an \(n\)th-order nonlinear neutral delay differential equation. (English) Zbl 0757.34058

J. Comput. Appl. Math. 41, No. 1-2, 35-40 (1992).
The authors study the neutral delay differential equation \[ [y(t)+P(t)y(g(t))]^{(n)}+\delta Q(t)f(y(h(t)))=0,\qquad n\geq 1,\quad t\geq t_ 0>0,\tag{E} \] where \(\delta=\pm 1\), \(P,Q,g,h: [t_ 0,\infty)\to R_ +\) are continuous functions, \(g(t)\leq t\), \(h(t)\leq t\), \(g(t)\to \infty\), \(h(t)\to\infty\) as \(t\to\infty\); \(f: R\to R\) is continuous with \(uf(u)>0\) for \(u\neq 0\). This paper contains two theorems which give sufficient conditions under which any (bounded) solution of (E) is either oscillatory or \(y(t)\to 0\) as \(t\to\infty\).
Reviewer: P.Marušiak (Žilina)

Cited in 6 Documents

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K40 Neutral functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

neutral delay differential equation; oscillatory
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\textit{J. R. Graef} and \textit{P. W. Spikes}, J. Comput. Appl. Math. 41, No. 1--2, 35--40 (1992; Zbl 0757.34058)
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References:

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