Abstract
In this paper, a nonlinear competitive system with two parameters is considered. By constructing a curve , we divide the parameters space into two disjoint subsets and . Furthermore, we obtain the sufficient conditions on the existence of the positive periodic solutions in and on by using the method of upper and lower solutions and the degree theory. More specifically, for the competitive system, there are at least two positive periodic solutions for , at least one positive periodic solution for , and no positive periodic solution for .
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