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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) h a(t)− n X i=1 ai(t) Z 0 −Ti x(t+θ) dμi(θ)− m X j=1 bj(t) Z 0 −T̂j x′(t+θ) dνj(θ) i , where the coefficients a, ai, bj are continuous and periodic functions, with the same period. The values Ti, T̂j are positive, and the functions μi, νj are nondecreasing with R 0 −Ti dμi = 1 and R 0 −T̂j dνj = 1.