STRICTLY NONAUTONOMOUS COOPERATIVE SYSTEM WITH A 1ST INTEGRAL

The authors consider the nonautonomous cooperative system dx(i)/dt = F (i)(t, x1,..., x(n)) (i = 1,..., n) in the nonnegative orthant in the real n-dimensional Euclidean space, which has the first integral with positive gradient. The authors guess that every solution to such a eit her converges to an asymptotic state (for the almost periodic (or peri odic) case, this state is an almost periodic (or periodic) solution) o r eventually leaves any compact set. They partly prove this conjecture .