| 具有混合单调非线性项的四阶微分方程两点边值问题 |
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| 引用本文： | 宋姝,张玲玲.具有混合单调非线性项的四阶微分方程两点边值问题[J].数学的实践与认识,2020(8):178-185. |
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| 作者姓名： | 宋姝 张玲玲 |
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| 作者单位： | 山西工程职业学院基础部;太原理工大学数学学院 |
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| 基金项目： | 国家自然科学基金(11626165)。 |
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| 摘 要： | 讨论了一类具有混合单调非线性项的四阶微分方程两点边值问题,运用一类混合单调算子的不动点定理及"和型"非线性算子的不动点定理,结合单调迭代技巧和格林函数的性质,获得方程正解存在且唯一的充分条件,并构造两个迭代序列收敛于此唯一解.最后,给出具体的例子验证了定理的正确性.
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| 关 键 词： | 四阶微分方程 不动点定理 边值问题 正解 |
Two Point Boundary Value Problem of Fourth Order Differential Equation with Mixed Monotone Nonlinear Terms |
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| SONG Shu,ZHANG Ling-ling.Two Point Boundary Value Problem of Fourth Order Differential Equation with Mixed Monotone Nonlinear Terms[J].Mathematics in Practice and Theory,2020(8):178-185. |
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| Authors: | SONG Shu ZHANG Ling-ling |
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| Institution: | (Department of General Courses,Shanxi Engineering Vocational College,Taiyuan 030009,China;Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | In this paper,we discuss a class of two point boundary value problem of fourth order differential equation with mixed monotone nonlinear term.By using a class of fixed point theorems of mixed monotone operator and a sum type nonlinear operator,combining with monotone iterative technique and the properties of Green function,we obtain the sufficient conditions which guarantee the existence and uniqueness of positive solution,also we provide iterative sequences for approximating the solution.At last,a concrete example is listed to testify the theorem. |
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| Keywords: | fourth order differential equation fixed point theorem boundary value problem positive solution |
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