Global attractivity and ”level-crossings” in a periodic logistic integrodifferential equation. (English) Zbl 0758.45004
The purpose of this article is to derive sufficient conditions for the existence of a globally attractive positive periodic solution of the periodic logistic integrodifferential equation
\[
dN(t)/dt=N(t)[a(t)- b(t)\int^ \infty_ 0K(s)N(t-s)ds] \tag{*}
\]
using the stability properties of solutions of \((*)\), where \(a,b\) are continuous positive periodic functions of periodic \(\tau\) and \(K\) is a nonnegative integrable function defined on \(R^ +\) such that \(\int^ \infty_ 0K(s)ds=1\), \(\int^ \infty_ 0sK(s)ds\leq c<\infty\). Sufficient conditions for all positive solutions to have “level crossing” about the unique positive periodic solution are also derived.
Reviewer: S.Anita (Iaşi)
MSC:
| 45J05 | Integro-ordinary differential equations |
| 45M15 | Periodic solutions of integral equations |
| 45M20 | Positive solutions of integral equations |
Keywords:
level crossings; existence; globally attractive positive periodic solution; periodic logistic integrodifferential equationReferences:
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