| 一类四阶非线性微分方程边值问题解的存在性探究 |
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| 引用本文： | 成连连,郭红梅.一类四阶非线性微分方程边值问题解的存在性探究[J].通化师范学院学报,2013,34(8):10-12. |
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| 作者姓名： | 成连连 郭红梅 |
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| 作者单位： | 1. 山西体育职业学院,山西太原,030006
2. 山西生物应用职业技术学院 |
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| 摘 要： | 文中探讨了一类四阶非线性微分方程边值问题,并在一定条件下,利用上下解方法及不动点定理,得出此类问题解存在的充分条件.通过构造法将该边值问题转化为等价的积分方程,进而通过映射将积分方程转化为算子方程,并利用不动点定理证明了解的存在性.
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| 关 键 词： | 四阶微分方程 边值问题 上下解方法 存在性 |
Existence of Boundary Value Problem Solutions for a Class of Fourth Order Nonlinear Differential Equations |
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| CHENG Lian-lian
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GUO Hong-mei.Existence of Boundary Value Problem Solutions for a Class of Fourth Order Nonlinear Differential Equations[J].Journal of Tonghua Teachers College,2013,34(8):10-12. |
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| Authors: | CHENG Lian-lian GUO Hong-mei |
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| Institution: | CHENG Lian - lian1 , GUO Hong - mei2 ( 1. Shanxi Sports Vocational College, Taiyuan, Shanxi 030006, China ; 2. Shanxi Vocational and Technical College of Biological Applications) |
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| Abstract: | This paper discusses a class of fourth order nonlinear differential equation boundary value problem, and under certain conditions, the use of upper and lower solutions method and fixed point theorem, concluded that sufficient conditions of existence for the solution of such problems. By constructing method, the boundary value problem is converted into the equivalent equation is converted into the operator equation, and the point theorem. integral equation, then by mapping the integral existence of solution is proved by using the fixed |
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| Keywords: | fourth -order differential equation boundary value problem upper and lower solutions method existence |
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