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We consider a system x'=f(t ,x) of n first order differential equations, where all coordinate functions are weakly convex (or weakly concave ) in x. We have investigated how the closed solutions behave in subsets (of suitable form), in which the off-diagonal entries in the Jacobi matrix have fixed sign. The investigations have shown that it is possible to generalize an earlier (published) result in the case n=1 on the number of closed solutions. Furthermore, we have found some geometrical and topological properties of the set of initial points for closed solutions in a subset of the mentioned type. These results are in particular interesting in the cooperative (or the competitive) case.
StatusCurrent
Period01/01/96 → …
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ID: 2228346