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

Abstract 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 delays d x i ( t ) d t = x i ( t ) a i ( t ) - ∑ j = 1 n b ij ( t ) ∫ - T ij 0 K ij ( θ ) x j ( t + θ ) d θ - ∑ j = 1 n c ij ( t ) ∫ - T ˆ ij 0 K ˆ ij ( θ ) x j ′ ( t + θ ) d θ , i = 1 , 2 , … , n , where a i , b ij , c ij ∈ C ( R , R + ) (i, j = 1, 2, … , n) are ω-periodic functions, T ij , T ˆ ij ∈ ( 0 , ∞ ) (i, j = 1, 2, … , n) and K ij , K ˆ ij ∈ ( R , R + ) satisfying ∫ - T ij 0 K ij ( θ ) d θ = 1 , ∫ - T ˆ ij 0 K ˆ ij ( θ ) d θ = 1 , i, j = 1, 2, … , n.

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