Positive periodic solutions of periodic neutral Lotka–Volterra system with distributed delays

By using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka–Volterra system with distributed delaysdxi(t)dt=xi(t)ai(t)-∑j=1nbij(t)∫-Tij0Kij(θ)xj(t+θ)dθ-∑j=1ncij(t)∫-Tˆij0Kˆij(θ)xj′(t+θ)dθ,i=1,2,…,n,where ai,bij,cij∈C(R,R+)ai,bij,cij∈C(R,R+) (i, j = 1, 2, … , n) are ω  -periodic functions, Tij,Tˆij∈(0,∞) (i, j = 1, 2, … , n  ) and Kij,Kˆij∈(R,R+) satisfying ∫-Tij0Kij(θ)dθ=1,∫-Tˆij0Kˆij(θ)dθ=1, i, j = 1, 2, … , n.