Periodic solutions of a delayed, periodic logistic equation. (English) Zbl 1118.34327

Chen, Yuming

Appl. Math. Lett. 16, No. 7, 1047-1051 (2003).

Consider the delay differential equation
\[ {dN(t)\over dt}= N(t)[a(t)- b(t) N^p(t-\sigma(t))- c(t) N^q(t-\tau(t))],\tag{\(*\)} \]
where \(a\), \(b\), \(c\), \(\tau\) are continuous \(\omega\)-periodic functions, \(p\) and \(q\) are positive constants. The author establishes the existence of a positive \(\omega\)-periodic solution of \((*)\) by using Mawhin’s continuation theorem.

Reviewer: Klaus R. Schneider (Berlin)

MSC:

34K13	Periodic solutions to functional-differential equations
92D25	Population dynamics (general)

Keywords:

Positive periodic solution; Delayed logistic equation; Coincidence degree

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