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Zbl 0997.34075
Zhang, Zhengqiu; Wang, Zhicheng
Asymptotic behavior of solutions to neutral differential equations with positive and negative coefficients.
(English)
[J] Ann. Differ. Equations 17, No.3, 295-305 (2001). ISSN 1002-0942

Neutral delay differential equations of the form $$[x(t)+\lambda c(t)x(t-\sigma)]'+p(t)x(t-\tau)-Q(t)x(t-\delta)=0$$ are considered when $t\to \infty$, under the main conditions: $\lambda\in\{-1,1\}$, $\sigma>0$, $\tau, \delta \ge 0$, $c,p,Q\in C([t_0,\infty),\bbfR^+)$, and if there exists a constant $A>0$ such that $Q(t+\delta-\tau)\le Ap^*(t)$ with $p^*(t)=p(t)-Q(t+\delta-\tau)$ for $t\ge\max\{t_0,t_0+\tau-\delta\}$. Sufficient conditions are given for the validity of the statements: all oscillatory solutions are vanishing and all solutions are vanishing. Illustrative examples are considered, too.
[J.Diblík (Brno)]
MSC 2000:
*34K40 Neutral equations

Keywords: neutral equations; asymptotic behaviour; delay

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