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On almost periodic solutions of the competing species problems. (English) Zbl 0668.34042
Consider a system of n (\(\geq 2)\) competition equations of Volterra-Lotka type \[ (*)\quad x_ i'(t)=x_ i(t)[b_ i(t)- \sum^{m}_{j=1}a_{ij}(t)x_ j(t)], \] i\(=1,...,n\) with coefficients which are almost periodic in time. It was shown by K. Gopalsamy [J. Aust. Math. Soc., Ser. B 27, 346-360 (1986; Zbl 0591.92022)] that in general two independent conditions \((G_ 1)\) and \((G_ 2)\) are needed for the existance of a solution of (*) which is almost periodic and bounded below. In this paper it is shown that if \(n=2\), however, then \((G_ 1)\Rightarrow (G_ 2)\) so that only one condition is required.
Reviewer: F.M.Arscott

MSC:
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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