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Linearized oscillations for equations with positive and negative coefficients. (English) Zbl 0715.34125

Our aim is to present a linearized oscillation result for the neutral differential equation with positive and negative coefficients \[ \frac{d}{dt}[x(t)-P(t)G(x(t-\tau))]+Q_ 1(t)H_ 1(x(t-\sigma_ 1))- Q_ 2(t)H_ 2(x(t-\sigma_ 2))=0. \] Roughly speaking, we prove that under appropriate hypotheses, this nonlinear differential equation has the same oscillatory behavior as an associated linear equation with constant coefficients.
Reviewer: G.Ladas

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
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