Oscillations of a system of delay logistic equations. (English) Zbl 0686.34066
Summary: We obtain sufficient conditions for the oscillation of all positive solutions of the system
\[
\dot N_ i(t)=N_ i(t)[a_ i- \sum^{m}_{j=1}b_{ij}N_ j(t-\tau)],\quad i=1,2,...,m
\]
about its steady state. We also obtained sufficient conditions for the existence of a nonoscillatory solution of this system.
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 |
References:
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| [2] | Gopalsamy, K., Oscillatory properties of systems of first order linear delay differential inequalities, Pacific J. Math., 128, 299-305 (1987) · Zbl 0634.34054 |
| [3] | Györi, I.; Ladas, G., Oscillations of systems of neutral differential equations, J. Differential Integral Equations, 1, 281-286 (1988) · Zbl 0723.34057 |
| [4] | Ladas, G.; Stavroulakis, I. P., On delay differential inequalities of first order, Funkcial. Ekvac., 25, 105-113 (1982) · Zbl 0492.34060 |
| [5] | Tarski, A., A lattice theoretical fixed point theorem and its applications, Pacific J. Math., 5, 285-309 (1955) · Zbl 0064.26004 |
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