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Oscillation and asymptotic behavior of second order neutral differential equations. (English) Zbl 0647.34071
The authors consider the following second order differential equation \[ (1)\quad \frac{d^ 2}{dt^ 2}[y(t)+P(t)y(t-\tau)]+Q(t)y(t- \sigma)=0,\quad t\geq t_ 0,\quad \tau,\sigma \geq 0 \] with \(P,Q\in C([t_ 0,\infty],{\mathbb{R}})\), where the highest derivate of the unknown function appears both with delays \(\tau\) and \(\sigma\) in some terms and without delays in some others. Such equation is called neutral delay differential equation. In this paper the authors investigate the asymptotic behavior of the nonoscillatory solutions of (1) and find sufficient conditions for the oscillation of all solutions; of all bounded solutions; all unbounded solutions.
Reviewer: A.Laforgia

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
Full Text: DOI
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