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A linearized oscillation result for neutral delay differential equations. (English) Zbl 0805.34065

Summary: We consider the first order nonlinear neutral delay differential equation (1) \({d \over dt} (x(t) - P(t)g(x(t - \tau))) + Q(t)h(x(t - \sigma)) = 0\), and establish a linearized oscillation result of equation (1) when \(P(t) \geq 1\), which answers partially an open problem proposed by Györi and Ladas.

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
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References:

[1] Chuanxi, Hiroshima Math. J. 20 pp 331– (1990)
[2] Chuanxi, J. Math. Anal. Appl. 159 pp 237– (1991)
[3] and , Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991
[4] Linearized Oscillations for Neutral Equations, Differential Equation, Proceedings of the 1987 Equadiff Conference, Dekker, New York, pp. 379–387
[5] Ladas, J. Differential Equations 88 pp 238– (1990)
[6] Yu, PanAmerican Mathematical Journal
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