一类无限时滞微分方程特定周期解的存在性

Existence of Special Periodic Solution for a Kind of Indefinite Delay Differential Equation

利用相空间的理论和方法,研究了一类无限时滞微分方程:xi′(t)=iω(t,xi)[bi(t,xt)-ai(t,xt)xi(t)-∫-∞t Fi(t,s,x1(s),…,xn(s))ds],(i=1,…,n)特定周期解的存在性,并应用推广了Volterra型积分微分方程的周期解.

By use of phase sate theory and method, the existence of special periodic solution for a kind of indefinite delay differential equation：xi＇（t）=ωi（t,xi）[bi（t,xt）-ai（t,xt）xi（t）-∫-∞^tFi（t,s,x1（s）,…,xn（s））ds],（i=1,…,n） And the periodic solution for the Volterra-type integral differential equation was applied and spreaded.