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中文摘要：
考虑泛函微分方程u′（t）=a（t）u（t）-λb（t）f（u（t-τ（t）））正周期解的存在性,其中λ〉0为参数,a∈C（R,[0,∞））为ω-周期的,且∫ω0a（t）dt〉0;b,τ∈C（R,R）为ω-周期的.f∈C（[0,∞）,R）且f（0）〉0.在函数b变号的情形下,本文运用Leray-Schauder不动点定理,建立了上述泛函微分方程正周期解的存在性结果.
英文摘要：
We are concerned with the existence of positive periodic solutions of the following functional differential equation u′（t）=a（t）u（t）-λb（t）f（u（t-τ（t））） where λ0 is a parameter,a∈C（R,[0,∞）） is a ω-periodic and ∫ω0a（t）dt0;b,τ∈C（R,R） are ω-periodic.f∈C（[0,∞）,R） and f（0）0.By using Leray-Schauder fixed point theorem,we establish the existence results of positive periodic solutions for the above problem under the case that b may change its sign.
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