| 一类非线性三阶微分方程边值问题解的存在唯一性 |
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| 引用本文： | 杨景保,莫嘉琪.一类非线性三阶微分方程边值问题解的存在唯一性[J].应用数学和力学,2020(2):216-222. |
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| 作者姓名： | 杨景保 莫嘉琪 |
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| 作者单位： | 亳州学院教育系;安徽师范大学数学与统计学院 |
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| 基金项目： | 安徽省高校自然科学研究项目(KJ2017A702;KJ2019A1300;KJ2019A1303) |
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| 摘 要： | 研究了一类非线性三阶微分方程边值问题解的存在唯一性.首先分析了近年来国内外三阶微分方程边值问题的研究成果,提出了边值条件中含非线性函数的非线性三阶微分方程边值问题.然后寻找相关线性问题的解决途径,利用Banach不动点定理,证明了提出的边值问题存在唯一解.最后,举例阐述了主要结果的应用.
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| 关 键 词： | BANACH不动点定理 三阶微分方程 两点边值问题 |
Existence and Uniqueness of Solutions to Boundary Value Problems of a Class of Nonlinear 3rd-Order Differential Equations |
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| YANG Jingbao,MO Jiaqi.Existence and Uniqueness of Solutions to Boundary Value Problems of a Class of Nonlinear 3rd-Order Differential Equations[J].Applied Mathematics and Mechanics,2020(2):216-222. |
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| Authors: | YANG Jingbao MO Jiaqi |
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| Institution: | (Department of Education,Bozhou University,Bozhou,Anhui 236800,P.R.China;School of Mathematics&Statistics,Anhui Normal University,Wuhu,Anhui 241003,P.R.China) |
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| Abstract: | The existence and uniqueness of solutions to the boundary value problem of a class of nonlinear 3rd?order differential equations were studied.Firstly,the results of the research on the boundary values of 3rd?order differential equations at home and abroad in recent years were combed.Then the boundary value problem of nonlinear 3rd?order differential equations with nonlinear boundary value conditions was put forth,and the solution to the related linear prob?lem was explored.Finally,the Banach fixed point theorem was used to prove that the proposed boundary value problem has a unique solution.An example illustrates the applicability of the main results. |
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| Keywords: | Banach fixed point theorem 3rd?order differential equation 2?point boundary val?ue problem |
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