| 一类二阶常微分方程组边值问题解的存在唯一性 |
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| 引用本文： | 王丹,李永祥.一类二阶常微分方程组边值问题解的存在唯一性[J].四川大学学报(自然科学版),2021,58(4):041001-041001-5. |
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| 作者姓名： | 王丹 李永祥 |
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| 作者单位： | 西北师范大学,西北师范大学 |
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| 摘 要： | 本文讨论二阶常微分方程组边值问题
-u''(t)=f(t,u(t),v(t)),t∈0,1],
-v''(t)=g(t,u(t),v(t)),t∈0,1],
u(0)=u(1)=0,v(0)=v(1)=0
解的存在性与唯一性,其中f,g:0,1]×R×R→R连续.在非线性项f(t,x,y)与g(t,x,y)关联的不等式条件下,运用Leray-Schauder不动点定理,获得了该问题解的存在性及唯一性.
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| 关 键 词： | 二阶常微分方程组 边值问题 存在性与唯一性 Leray-Schauder不动点定理 |
| 收稿时间： | 2020/12/1 0:00:00 |
| 修稿时间： | 2021/1/8 0:00:00 |
Existence and uniqueness of solutions for boundary value problem of second-order nonlinear ordinary differential systems |
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| WANG Dan,LI Yong-Xiang.Existence and uniqueness of solutions for boundary value problem of second-order nonlinear ordinary differential systems[J].Journal of Sichuan University (Natural Science Edition),2021,58(4):041001-041001-5. |
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| Authors: | WANG Dan LI Yong-Xiang |
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| Institution: | Northwest Normal University,Northwest Normal University |
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| Abstract: | This paper discusses the existence and uniqueness of solutions for the boundary value problem of a class of nonlinear second-order ordinary differential system. By using the Leray-Schauder fixed point theorem, the existence and uniqueness of solutions is obtained. |
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| Keywords: | second order ordinary differential equations value problem existence and uniqueness Leray-Schauder fixed point theorem |
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