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

Zhang, B. G.

J. Math. Anal. Appl. 139, No. 2, 311-318 (1989).

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

Keywords:

oscillatory solution; first order neutral functional differential equations

References:

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