Convex and Concave Differential Systems

  • Sandqvist, Allan (Project Manager)
  • Andersen, Kurt Munk (Project Participant)

    Project Details


    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.
    Effective start/end date01/01/1996 → …