| 二阶Volterra型积分微分方程非线性边值问题的奇摄动 |
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| 引用本文： | 王国灿,金丽.二阶Volterra型积分微分方程非线性边值问题的奇摄动[J].大连铁道学院学报,2004,25(4):14-17. |
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| 作者姓名： | 王国灿 金丽 |
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| 作者单位： | 大连交通大学数理系 辽宁 大连 116028
(王国灿)，大连交通大学数理系 辽宁 大连 116028(金丽) |
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| 摘 要： | 利用微分不等式理论研究了二阶Volterra型积分微分方程非线性边值问题的解的存在性和唯一性．以上下解为基础，建立了解的唯一性定理，在适当条件下，构造具体的上下解，得到了解的存在性和唯一性．结果表明这种技巧为奇摄动边值问题的存在性和唯一性研究提出了新的思路。
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| 关 键 词： | Volterra型积分微分方程 非线性边值问题 奇摄动 二阶 解的存在性 上下解 唯一性 思路 技巧 条件 |
Singularly Perturbed Second Order Volterra type Integro-differential Nonlinear Boundary Value Problem |
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| WANG Guo-can,JIN Li.Singularly Perturbed Second Order Volterra type Integro-differential Nonlinear Boundary Value Problem[J].Journal of Dalian Railway Institute,2004,25(4):14-17. |
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| Authors: | WANG Guo-can JIN Li |
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| Abstract: | The existence and uniqueness of solution for nonlinear boundary value problem of Volterra type integro-differential equation by means of differential inequality theories are studied.Based on upper and lower solutions,the existence and uniqueness theorem are established. Specific upper and lower solutions are constructed,and their solutions are obtained.The result shows the techniques to be new to apply in solving the existence and uniqueness of singularly perturbed boundary problem. |
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| Keywords: | singularly perturbation nonlinear boundary value problem upper and lower solution estimate of solutions |
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