Positive periodic solutions of periodic neutral Lotka–Volterra system with state dependent delays

By using a fixed point theorem of strict-set-contraction, some new criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka–Volterra system with state dependent delays dxi (t) dt = xi (t) ri (t)− n j=1 aij (t)xj (t) − n j=1 bij (t)xj t − τij t,x1(t ), . . . , xn(t) − n j=1 cij (t)x j t −σij t,x1(t ), . . . , xn(t) , i= 1, 2, . . . , n, where ri, aij , bij , cij ∈ C(R,R+) (i, j = 1, 2, . . . , n) are ω-periodic functions and τij ,σij ∈ C(Rn+1,R) (i = 1, 2, . . . , n) are ω-periodic functions with respect to their first arguments, respectively. © 2006 Elsevier Inc. All rights reserved.