| 中立型标量积分微分方程的周期解 |
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| 引用本文： | 陈凤德,孙德献,陈晓星.中立型标量积分微分方程的周期解[J].数学研究,2003,36(4):345-350. |
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| 作者姓名： | 陈凤德 孙德献 陈晓星 |
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| 作者单位： | 福州大学数学系,福建,福州,350002 |
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| 基金项目： | The author is supported by the Fundation of Ability Person of Fuzhou Univcrsity by the
grants(0030824228)，the Fundation of Developing Science and Technology of Fuzhou University under
the grants 2003-XQ-21，the Foundation of Fujian Education Bureau |
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| 摘 要： | 本文考虑中立型标量方程x′(t)=a(t)x(t)+∫
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| 关 键 词： | 周期解 存在性 唯一性 无穷时滞 中立型积分微分方程 |
Periodic Solutions of Scalar Neutral Integro-Differential Equation |
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| Abstract.Periodic Solutions of Scalar Neutral Integro-Differential Equation[J].Journal of Mathematical Study,2003,36(4):345-350. |
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| Authors: | Abstract |
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| Abstract: | This paper deals with the existence and uniqueness of periodic solutions of scalar neutral integro-differential equation with infinite delay of the form x′(t)=a(t)x(t)+∫t-∞g(t,s,x(s))ds+∫t-∞h(t,s,x′(s))ds+f(t,x(t))where a is continuous function, f is continuous function on R×R, g(t,s,x) and h(t,s,x) are continuous functions on R×R×R, also a(t+T)=a(t), g(t+T, s+T, x)=g(t,s,x), h(t+T, s+T, x)=h(t,s,x), f(t+T, x)=f(t,x). The sufficient conditions for the existing unique periodic solution of the equation are obtained by using functional analysis method and the estimated formulas of solutions of the linear scalar system. |
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| Keywords: | Periodic solution Existence Uniqueness Infinite delay Neutral integro-differential equation |
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