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Zbl 1025.34065
Zhou, Yong; Zhang, B.G.
Existence of nonoscillatory solutions of higher-order neutral differential equations with positive and negative coefficients.
(English)
[J] Appl. Math. Lett. 15, No.7, 867-874 (2002). ISSN 0893-9659

The authors consider the following higher-order neutral functional-differential equations with positive and negative coefficients: $$\frac{d^n}{dt^n}[x(t)+cx(t-\tau)]+(-1)^{n+1}[P(t)x(t-\sigma)-Q(t)x(t-\delta)]=0,\quad t\geq t_0,$$ where $n\geq 1$ is an integer, $c\in \bbfR, \tau, \sigma, \delta \in\bbfR^+$, and $P, Q\in C([t_0, \infty), \bbfR^+), \bbfR^+=[0, \infty)$. They obtain global results (with respect to $c$) which are some sufficient conditions for the existence of nonoscillatory solutions.
[Yongkun Li (Kunming, Yunnan)]
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: neutral differential equations; nonoscillatory solution; existence

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