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Characteristic multipliers and stability of symmetric periodic solutions of \(\dot x(t)=g(x(t-1))\). (English) Zbl 0672.34069
The equation (1) \(\dot x(t)=g(x(t-1))\) is considered where g is an odd and monotone nonlinear function. It is proved that for a certain class of such functions the nontrivial characteristic multipliers of any periodic solution of (1) satisfying \(x(t)=-x(t-2)\), \(t\in R\), are all strictly inside the unit circle.
Reviewer: R.G.Koplatadze

MSC:
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K20 Stability theory of functional-differential equations
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