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Permanence and stability in non-autonomous logistic systems with infinite delay. (English) Zbl 1035.34086

Here, the permanence, extinction and globally asymptotical stability for the nonautonomous logistic-type system with infinite distributed delay and time-dependent discrete delay of the form \[ {x^{\prime }\left( t\right) =x\left( t\right) \left[ \alpha \left( t\right) -d\left( t\right) x\left( t\right) -b\left( t\right) x\left( t-\tau \left( t\right) \right) -c\left( t\right) \int_{-\infty }^{0}k\left( s\right) x\left( t+s\right) ds\right] }\tag{1} \] is studied. An open question proposed by G. Seifert [Differ. Integral Equ. 9, 335–342 (1996; Zbl 0838.34083)].

MSC:

34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations

Citations:

Zbl 0838.34083
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References:

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