具有无穷时滞泛函微分方程的周期解  

PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

作　　者：彭世国[1] 朱思铭[2] 

机构地区：[1]广东工业大学应用数学系,广州510090 [2]中山大学数学系,广州510275

出　　处：《数学年刊（A辑）》2002年第3期371-380,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19771089)资助的项目.

摘　　要：讨论具有无穷时滞中立型泛函微分方程的周期解问题.利用矩阵测度和Krasnoselskii不动点定理得到了周期解的存在性和唯一性定理;特别地,当Q（s）为零矩阵,A（t,x）=A（t）时给出了存在唯一稳定的周期解的条件.Discuss the periodic solutions of neutral functional differential equations with infinite delay of the followingd/dt(x(t) -∫-∞o Q(s)x(t + s)ds) = A(t, x(t))x(t) + f(t, xt).Some results on the existence and uniqueness of periodic solutions are obtained by using matrix measure and Krasnoselskii's fixed theorem. Especially, when Q(s) ≡ 0 and A(t, x) = A(t), the conditions which guarantee the existence of unique and stable periodic solutions are derived.

关 键 词：无穷时滞 中立型 泛函微分方程 周期解 

分 类 号：O175.12[理学—数学]