Oscillation of first order neutral functional differential equations. (English) Zbl 0683.34037

The author obtains some new sufficient conditions for oscillation of the following first order neutral functional differential equations \[ (x(t)+cx(t-\tau))'-\sum^{n}_{i=1}p_ ix(t-\tau_ i)=0,\quad t\geq t_ 0, \] and \[ (x(t)-cx(t-\tau))'+P(t)x(t-\sigma)=0,\quad t\geq t_ 0 \] where \(\tau,\sigma,\{\tau_ i\}^ n_{i=1}\) are positive delays, \(p_ i\in R^*_+\), and P(t) is periodic with period \(\tau\).
Reviewer: T.Havarneanu


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
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[1] Grammatikopoulos, M.K; Grove, E.A; Ladas, G, Oscillations of first order neutral delay differential equations, J. math. anal. appl., 120, 510-520, (1986) · Zbl 0566.34056
[2] Koplatadze, R.G; Canturija, T.A; Koplatadze, R.G; Canturija, T.A, On the oscillatory and monotone solutions of the first order differential equations with deviating arguments, Differentsial’nye uravneniya, Differentsial’nye uravneniya, 18, 1472-1465, (1982) · Zbl 0496.34044
[3] Kulenovic, M.R.S; Ladas, G; Meimaridou, A, Necessary and sufficient condition for oscillations of neutral differential equations, J. austral. math. soc. ser. B, 28, 362-375, (1987) · Zbl 0616.34064
[4] Ladas, G; Sficas, Y.G, Oscillations of neutral delay differential equations, canad. math. bull. T. 29 F.4, 438-445, (December 1986)
[5] Ladas, G, Sharp conditions for oscillations caused by delays, Appl. anal., 95-98, (1979) · Zbl 0407.34055
[6] Lakshmikantham, V; Ladde, G.S; Zhang, B.G, Oscillation theory of differential equations with deviating arguments, (1987), Dekker New York · Zbl 0832.34071
[7] Jiong, Ruan, On the oscillation of neutral differential difference equations with several delays, Sci. sinica A.N., 5, 467-477, (1986)
[8] Zhang, B.G, A survey of the oscillation of solutions to first order differential equations with deviating arguments, (), 475-483
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