Positive periodic solutions of neutral logistic equations with distributed delays
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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)[α(t) - ∑ni=1 αi(t) ∫0-Ti x(t+θ) dμi(θ) = ∑mj=1 bj(t) ∫0-T̂j x′(t+θ) dvj(θ)],
where the coefficients α, αi, bj are continuous and periodic functions, with the same period. The values Ti, T̂j are positive, and the functions μi, vj are non-decreasing with ∫0-Ti dμi = 1 and ∫0-T̂i dvj = 1.
CitationLi, Y., Wang, G., & Wang, H. (2007). Positive periodic solutions of neutral logistic equations with distributed delays. Electronic Journal of Differential Equations, 2007(13), pp. 1-10.
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