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Periodicity in a logistic type system with several delays. (English) Zbl 1061.34050
Summary: With the help of a continuation theorem based on Gaines and Mawhin’s coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following logistic-type system with several delays $\frac{du(t)}{dt}=u(t)\left[a(t)-\sum^m_{j=1}b_j(t) \biggl(u\bigl(t-\tau_j(t)\bigr)\biggr)^{\theta_j} \right],$ where $$a(t)$$, $$b_j(t)$$ are positive periodic continuous functions with periodic $$\omega>0$$, $$\tau_j(t)$$ are nonnegative continuous periodic functions with periodic $$\omega>0$$. After that, by constructing a suitable Lyapunov functional, some sufficient conditions which guarantee the stability of the positive periodic solutions are obtained.

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