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Extension of Hunt and Yorke’s conjecture. (Chinese. English summary) Zbl 0794.34059

Summary: We consider the neutral differential equation \({d\over dt} [x(t)- P(t)x(t-\tau)]+ Q(t)x(t-\sigma)=0\), \(t\geq t_ 0\), where \(P\), \(Q\in C([t_ 0,+\infty), R^ +)\) and \(\tau\), \(\sigma\in R^ +\). We establish sufficient conditions for oscillation of the equations. Our conditions are “sharp” in the sense that when the coefficients \(P\) and \(Q\) are constants they are also necessary. Our results extend and improve some theorems.

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K40 Neutral functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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