On positive periodic solutions of Lotka-Volterra competition systems with deviating arguments

By using Krasnoselskii’s fixed point theorem, we prove that the following periodic n − n- species Lotka-Volterra competition system with multiple deviating arguments ( ∗ ) x ˙ i ( t ) = x i ( t ) [ r i ( t ) − ∑ j = 1 n a i j ( t ) x j ( t − τ i j ( t ) ) ] , i = 1 , 2 , … , n , {equation*} ( ) ẋ_i(t)=x_i(t) [r_i(t)-∑ ⱼ₌₁ⁿaᵢⱼ(t)x_j(t-τ ᵢⱼ(t)) ], i=1, 2, … , n, {equation*} has at least one positive ω − ω - periodic solution provided that the corresponding system of linear equations ( ∗ ∗ ) ∑ j = 1