| 具无穷时滞中立型周期微分系统的周期解 |
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| 引用本文： | 张丽娟,斯力更.具无穷时滞中立型周期微分系统的周期解[J].黑龙江大学自然科学学报,2006,23(4):462-469. |
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| 作者姓名： | 张丽娟 斯力更 |
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| 作者单位： | 烟台大学,数学与信息科学系,山东,烟台,264005;内蒙古师范大学,数学系,内蒙古,呼和浩特,010022 |
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| 摘 要： | 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.
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| 关 键 词： | 周期微分系统 中立型 无限时滞 周期解 不动点定理 |
| 文章编号： | 1001-7011(2006)04-0462-08 |
| 修稿时间： | 2006年1月17日 |
Periodic solutions of neutral periodic differential system with infinite delay |
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| ZHANG Li-juan,SI Li-geng.Periodic solutions of neutral periodic differential system with infinite delay[J].Journal of Natural Science of Heilongjiang University,2006,23(4):462-469. |
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| Authors: | ZHANG Li-juan SI Li-geng |
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| Abstract: | 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]. |
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| Keywords: | periodic differential system neutral infinite delay periodic solution fixed point Theorem |
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