| 具无限时滞的非线性积分微分方程的周期解 |
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| 引用本文： | 陈凤德.具无限时滞的非线性积分微分方程的周期解[J].应用数学学报,2003,26(1):141-148. |
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| 作者姓名： | 陈凤德 |
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| 作者单位： | 福州大学数学系,福州,350002;北京大学数学科学学院,北京,100871 |
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| 基金项目： | 福州大学校人才基金(0030824228)资助项目 |
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| 摘 要： | 本文考虑具无限时滞非线性积分微分方程和其中t∈R,T≥0是常数,x∈Rn;A(t,x),C(t,s)为n×n连续的函数矩阵;f(t,x),g(t,x),b(t)是n维连续向量.本文利用线性系统的指数型二分性理论和不动点定理研究此系统,建立了保证其周期解存在性.唯一性的充分条件.得到了一些新的结果,推广了相关文献的主要结果.
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| 关 键 词： | 无限时滞 非线性积分微分方程 周期解 周期系统 指数型二分性 不动点 |
PERIODIC SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATIONS WITH INFINITE DELAY |
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| CHEN FENGDE.PERIODIC SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATIONS WITH INFINITE DELAY[J].Acta Mathematicae Applicatae Sinica,2003,26(1):141-148. |
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| Authors: | CHEN FENGDE |
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| Abstract: | In this paper, nonlinear integrodifferential equations with infinite delay of the form.
are considered, where the n x n matrix function A(t, x) and the n- vectors f(t,x),g(t,x) are continuous in (t,x) R x .Rn, C(t,s) C(R x R). By combinning the theory of exponential dichotomies of linear system and fixed point theorem, some sufficient condition that guarantee the existence and uniqueness of periodic solution of the system (1) and (2) are obtained. Some new results are obtained. |
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| Keywords: | Infinite delay periodic solution existence uniqueness exponential dichotomies |
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