一类时标上具状态依赖时滞的中立型泛函微分方程的周期正解

Positive Periodic Solutions of Neutral Functional Differential Equations with State Dependent Delays on Time Scales

该文利用一个严格集压缩不动点定理,得到了如下形式的一类时标上具状态依赖时滞的中立型泛函微分方程周期正解存在性的充分条件x~Δ(t)=x(t)[r(t)-a(t)x(t)-sum from j=1 to n a_j(t)x(t-Υ_j(t,x(t)))-sum from j=1 to n c_j(t)x~Δ(t-σ_j(t,x(t)))],其中r,a,a_j,c_j∈C(T,R^+)(j=1,2,…,n)是ω-周期函数,Υ_j,σ_j∈C(T×R,T)(j=1,2,…,n)分别是其第一变元的ω-周期函数.

By using a fixed point theorem on strict-set-contraction,some sufficient conditionsare obtained for the existence of positive periodic solutions for a periodic neutral functionaldifferential equation on time scales of the formx^Δ（t）=x（t）[r（t）-a（t）x（t）-sum from j=1 to n aj（t）x（t-Υj（t,x（t）））-sum from j=1 to n cj（t）x~Δ（t-σj（t,x（t）））],where r,a,aj,cj∈C（T,R^＋）（j=1,2,…,n） areω-periodic functions,andτj,σj∈C（T×R,T）（j=1,2,…,n） areω-periodic functions with respect to their first arguments,respectively.