Some New Results of Nonautonomous Lotka]Volterra Competitive Systems with Delays1

In this paper, we improve and generalize the results of Montes de Oca and Zeeman w J. Math. Anal. Appl. 192 1995., 360]370; Proc. Amer. Math. Soc. 124 1996., 3677]3687x to general N-species nonautonomous Lotka]Volterra type competitive systems with finite or infinite delays. We establish a series of criteria under which a part of the n species of the systems is driven to extinction while the remaining part of the n species is persistent or uniformly persistent, or coexists globally asymptotically stable