Global attractivity and oscillations in a periodic delay-logistic equation. (English) Zbl 0711.34090

Zhang, B. G.; Gopalsamy, K.

J. Math. Anal. Appl. 150, No. 1, 274-283 (1990).

The authors present two theorems for the delay-logistic equation \(\dot x(t)=r(t)x(t)[1-x(t-n\tau)/K(t)].\) One is about sufficient conditions for the global attractivity of a periodic solution when r and K are positive periodic functions of period \(\tau\) and the other about those for the oscillation of all solutions about K when K is \(\tau\)-periodic but r non- periodic. A similar problem when the time delay is not \(n\tau\) remains open.

Reviewer: Ge Weigao

MSC:

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

Keywords:

delay-logistic equation; global attractivity

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