| Banach空间中二阶积-微分方程初值问题的解 |
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| 引用本文： | 宋光兴.Banach空间中二阶积-微分方程初值问题的解[J].数学学报,2004,47(1):71-78. |
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| 作者姓名： | 宋光兴 |
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| 作者单位： | 石油大学数学系,东营,257061 |
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| 基金项目： | 石油大学(华东)校基金资助项目(Y000804) |
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| 摘 要： | 利用半序方法和新的比较结果,研究了Banach空间中二阶积-微分方程初值问题的最大解、最小解、解的存在与相应解的迭代逼近.本文结果仅使用了下解或上解以及某些较弱的条件,并推广和改进了某些已知结果(见文1-10]).
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| 关 键 词： | 积-微分方程 解 单调迭代方法 |
| 文章编号： | 0583-1431(2004)01-0071-08 |
The Solutions of Initial Value Problems for Second Order Integro-Differential Equations in Banach Spaces |
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| Guang Xing SONG.The Solutions of Initial Value Problems for Second Order Integro-Differential Equations in Banach Spaces[J].Acta Mathematica Sinica,2004,47(1):71-78. |
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| Authors: | Guang Xing SONG |
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| Institution: | Guang Xing SONG (Department of Mathematics, University of Petroleum, Dongying 257061, P. R. China) |
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| Abstract: | By using the partial order method and some new comparison results, the maximal or minimal solutions, the unique solution and the iterative approximation of solutions of the initial value problem for nonlinear second order integro-differential equations in Banach spaces are investigated. In this paper, we require only a lower solution or an upper solution and some weaker conditions presented here, and we extend and improve some recent results (see 1-10]). |
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| Keywords: | Integro-differential equation Solution Monotone iterative technique |
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