具无穷时滞中立型周期微分系统的周期解(英文)

Periodic solutions of neutral periodic differential system with infinite delay

讨论了具无穷时滞中立型周期微分系统ddt(x(t)-∫-0∞Q(s)x(t+s)ds)=A(t,x(t-r(t)))x(t)+∫-0∞C(t,s)x(s)ds+f(t,xt)+b(t)的周期解问题.引入BCh空间,并利用矩阵测度和Krasnoselskii不动点定理,得到了此系统周期解的存在定理.特别地,当A(t,x)=A(t)时,给出了存在唯一周期解的条件.所得结论推广了相应文献的结果.

The existence and uniqueness of periodic solutions of the following neutral periodic differential system with infinite delay are inverstigated. d/dt（x（t）-∫^0 -∞ Q（s）x（t＋s）ds）=A（t,x（t-r）t）））x（t）＋∫^0 -∞ C（t,s）x（s）ds＋f（t,xt）＋b（t）.By introducing BCh space, and using matrix measure and Krasnoselskii＇ s fixed point Theorem, some sufficient conditions on the existence of periodic solutions to this system are obtained. Especially, when A （t,x） = A （t）, the conditions which guarantee the existence of unique periodic solution are derived. The obtained results generalize the corresponding results of [ 7,1,8,3,5 ].