| Banach空间中一类具有无穷时滞泛函积分微分方程解的存在性 |
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| 引用本文： | 傅显隆,张书年.Banach空间中一类具有无穷时滞泛函积分微分方程解的存在性[J].上海交通大学学报,2001,35(12):1908-1911. |
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| 作者姓名： | 傅显隆 张书年 |
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| 作者单位： | 上海交通大学,应用数学系, |
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| 基金项目： | 国家自然科学基金资助项目(19831030) |
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| 摘 要： | 讨论了Banach空间中一类具有无穷时滞泛函积分微分方程解的局部存在性和整体存在性。利用算字半群和无穷时滞理论以及Schauder不动点定理证明了方程解的局部存在性。引入一个适当的不等式条件，并利用解的延拓性质获得了整体存在性。所得结果推广了这类方程解的存在性的已有结论。
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| 关 键 词： | 泛函积分微分方程 无穷时滞 C0－半群 温和解 解 存在性 |
| 文章编号： | 1006-2467(2001)12-1908-04 |
| 修稿时间： | 2000年9月29日 |
Existence of Solutions for a Functional Integro-Differential Equation with Un
bounded Delay in Banach Space |
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| FU Xian long,ZHANG Shu nian.Existence of Solutions for a Functional Integro-Differential Equation with Un
bounded Delay in Banach Space[J].Journal of Shanghai Jiaotong University,2001,35(12):1908-1911. |
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| Authors: | FU Xian long ZHANG Shu nian |
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| Abstract: | This paper mainly discussed the local existence and global existence of solutions for a functional integro differential equation with unbounded delay in Banach space. Firstly, by applying the theory of operator semigroups and the theory of phase space for unbounded delays and by using Schauder's fixed point theorem and extension property of solutions, it discusses the local existence of solutions for the equation. Then by introducing a proper inequality condition and by using the extension property of solutions it obtains the global existence of solutions. The obtained results extend the results on the existence of solutions for this type of equations. |
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| Keywords: | functional integro differential equation unbounded delay C 0 semigroup mild solution existence of solutions |
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