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Stable steady state of some population models. (English) Zbl 0744.34071
Applying an analytical method and limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibrium $K$ for the equation (1) $\dot x(t)=-\gamma x(t)+D(x\sb t)$ which is the general form of many population models. The authors also investigate when an equilibrium for the functional differential equation (1) is uniformly stable, asymptotically stable, or uniformly asymptotically stable. Applications of the results to some population models are also presented.
Reviewer: S.Anita (Iaşi)

##### MSC:
 34K20 Stability theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations 92D25 Population dynamics (general)
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##### References:
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