## 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

### MSC:

 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
Full Text:

### References:

 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.