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Oscillations of neutral differential equations with variable coefficients. (English) Zbl 0682.34049
Summary: We obtain sufficient conditions for the oscillation of all solutions of the neutral differential equation \[ \frac{d}{dt}[y(t)+P(t)y(t- \tau)]+Q(t)y(t-\sigma)=0 \] where \(P,Q\in C[[t_ 0,\infty),{\mathbb{R}}]\) and \(\tau\), \(\sigma \in {\mathbb{R}}^+\). Our results extend and improve several known results in the literature. These improvements and extensions are obtained by establishing and using some lemmas which are interesting in their own rights and which may have further applications in analysis.

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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