| 关于2n阶常微分方程两点边值问题解的存在性与唯一性 |
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| 引用本文： | 裴明鹤. 关于2n阶常微分方程两点边值问题解的存在性与唯一性[J]. 系统科学与数学, 1997, 17(2): 165-172 |
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| 作者姓名： | 裴明鹤 |
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| 作者单位： | 吉林师范学院数学系!吉林，132011 |
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| 摘 要： | 本文利用Leray－Schauder度理论建立了一类2n阶非线性常微分方程两点边值问题解的存在性与唯一性定理，以及利用Fredholm择一原理与Fourier展式，建立了一类2n阶线性常微分方程两点边值问题解的存在性唯一性定理．
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| 关 键 词： | 2n阶常微分方程 两点边值问题 存在性 唯一性 |
ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONSOF TWO-POINT BOUNDARY VALUE PROBLEMS FOR 2nTH-ORDER DIFFERENTIAL EQUATIONS |
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| Ming He PEI. ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONSOF TWO-POINT BOUNDARY VALUE PROBLEMS FOR 2nTH-ORDER DIFFERENTIAL EQUATIONS[J]. Journal of Systems Science and Mathematical Sciences, 1997, 17(2): 165-172 |
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| Authors: | Ming He PEI |
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| Affiliation: | Department of Mathematics of Jinn Teacher's College, Jilin 132011 |
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| Abstract: | In this paper, first by using the Leray-Schauder degree theory we estabilishthe existence and uniqueness theorems of two-point boundary value problems for a class of2nth-order nonlinear differential equations, and then by using the Fredholm alternative andthe Fourier expansions, we estabilish the existence and uniqueness theorems of the solutions oftwo-point boundary value problems for a class of 2nth-order linear differential equations. |
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| Keywords: | 2nth-order differential equation two-point boundary value problem existence 9 uniqueness. |
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