| 四阶非线性常微分方程非线性两点边值问题解的存在唯一性 |
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| 引用本文： | 裴明鹤.四阶非线性常微分方程非线性两点边值问题解的存在唯一性[J].高校应用数学学报(A辑),1995(3):285-294. |
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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 |
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| 摘 要： | 本文利用Ｂｏｌｚａｎｏ定理，给出了四阶非线性常微微分方程具有非线性边界条件的两点边值问题（１）（２）２，（１）（２）３存在解与存在唯一解的一般性结果，并将所得结果应用于Ｌｉｐｓｃｈｉｚ方程，对Ｌｉｐｓｃｈｉｔｚ方程满足边界条件（２）２，（２）３的边值问题给出了存在解与存在唯一解的具体的充分条件。
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| 关 键 词： | 非线性 常微分方程 两点边值问题 存在性 解 |
EXISTENCE AND UNIQUENESS OF SOLUTIONS OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS FOR FOURTH-ORDER NONLINEAR DIFFERENTIAL EQUATIONS |
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| Pei Minghe.EXISTENCE AND UNIQUENESS OF SOLUTIONS OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS FOR FOURTH-ORDER NONLINEAR DIFFERENTIAL EQUATIONS[J].Applied Mathematics A Journal of Chinese Universities,1995(3):285-294. |
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| Authors: | Pei Minghe |
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| Abstract: | By using the Bolzano's theorem,this paper gives some general results of the existence and uniqueness of solutions of nonlinear two-point boundary value problems for fourth-order nonlinear differential equations,i.e.(1)(2)and (1)(3).With application of the obtained results to Lipschitz equations,we get concrete sufficient conditions of the existence and uniqueness of solutions of boundary problems with boundary value conditions (2) and (3) for Lipschitz equations. |
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| Keywords: | Fourth-order Nonlinear Differential Equation Two-point Boundary Value Problems Existence Uniqueness |
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