Extinction in nonautonomous competitive Lotka–Volterra systems with infinite delay

The principle of competitive exclusion is extended to nn-species nonautonomous Lotka–Volterra competition systems of differential equations with infinite delay. It is shown that if the coefficients are bounded, continuous and satisfy certain inequalities, then any solution with initial function in an appropriate space will have n−1n−1 of its components tend to zero, while the remaining one will stabilize at a certain solution of a logistic differential equation.