Positive periodic solutions of neutral logistic equations with distributed delays

Using a fixed point theorem of strict-set-contraction, we establish criteria for the existence of positive periodic solutions for the periodic neutral logistic equation, with distributed delays, x′(t) = x(t)[a(t)-∑_i=1ⁿa_i(t)∫ _-Ti⁰x(t+θ)dμ_i(θ)-∑ _j=1^mb_j(t)∫_-T̂j ⁰x′(t+θ)dv_j(θ), where the coefficients a, a_i, b_j are continuous and periodic functions, with the same period. The values T_i,T̂_j are positive, and the functions μ_i,v_j are nondecreasing with ∫_-Ti⁰ dμ_i = 1 and ∫ _-Ti⁰dv_j = 1.