Authors’ abstract: An n-species nonautonomous competitive Lotka-Volterra system is considered. The average conditions on the coefficients are given to guarantee that all but one species are driven to extinction. The generalization for the result is presented, i.e., for each the average conditions on the coefficients are presented to guarantee that of the species of the system are permanent while the remaining species are driven to extinction.
It is shown that these average conditions are improvement of those of S. Ahmad and F. Montes de Oca [Appl. Math. Comp. 90, 155–166 (1998; Zbl 0906.92024)] and F. Montes de Oca and M. L. Zeeman [Proc. Am. Math.Soc. 124, 3677–3687 (1996; Zbl 0866.34029) and J. Math. Anal. Appl. 192, 360–370 (1995; Zbl 0830.34039)].