一阶泛函微分方程正周期解的分歧结构

The Bifurcation Structure of Positive Periodic Solutions for the First-Order Functional Differential Equations

利用分歧理论,研究了一阶泛函微分方程u′(t)+a(t)u(t)=λh(t)f(u(t-τ(t)))t∈R正周期解的存在性,其中a,h∈C(R,[0,∞)),τ∈C(R,R),且a,h,τ均为T-周期函数.在[0,T]上,a,h≠0;f∈C([0,∞),[0,∞));当u>0时,f(u)>0;λ>0是一个参数.

This paper uses the bifurcation theory to show the existence of positive periodic solutions of the first-order functional differential equation u′（t）＋a（t）u（t）=λh（t）f（u（t-τ（t））） t ∈R where a,h ∈C（R,[0,∞））,τ ∈C（R,R）,and a,h,τare T-periodic functions,a,h≠0 on[0,T];f ∈ C（[0,∞）,[0,∞））,f（u）〉0,for u〉 0;λ〉 0 is a parameter.