Average Conditions For Permanence And Extinction In Nonautonomous Single-Species Kolmogorov Systems

The nonautonomous single-species Kolmogorov system is studied in this paper. Average conditions are obtained for permanence, global attractivity and extinction in the system. Applications of our main results to logistic equation and generalized logistic equation are given. It is shown that our average conditions are improvement of those in Vance and Coddington [J. Math. Biol. 27 (1989) 491-506] and some published literature on the system.