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Stability and uniqueness of slowly oscillating periodic solutions to Wright’s equation. (English) Zbl 1382.34069
In this paper by using a computer-assisted proof it is shown that, for any \(\alpha\) in the interval \([1.9, 6.0]\), Wright’s equation \[ y'(t)=-\alpha y(t-1)[1+y(t)] \] admits a unique slowly oscillating periodic solution \(y\), i.e., a continuous periodic function \(y(t)\) with the following property: There exist \(q\), \(\overline{q}>1\) such that up to a time translation, \(y(t)>0\) for \(0<t<q\), \(y(t)<0\), for \(q<t<q+\overline{q}\), and \(y(t+q+\overline{q})=y(t)\), for all \(t\).

MSC:
34K13 Periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
Software:
INTLAB; Matlab
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References:
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