| 一类三阶微分方程组多点边值问题解的存在性 |
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| 引用本文： | 谢淳,罗治国.一类三阶微分方程组多点边值问题解的存在性[J].大学数学,2011,27(4):57-62. |
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| 作者姓名： | 谢淳 罗治国 |
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| 作者单位： | 1. 湖南人文科技学院数学系,湖南娄底,417000
2. 湖南师范大学数学系,湖南长沙,410081 |
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| 基金项目： | 国家自然科学基金项目，湖南省教育厅重点项目 |
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| 摘 要： | 利用拓扑度理论和上下解方法讨论了一类三阶微分方程组{x′′′（t）＋f1（t,y（t）,x′（t）,x″（t））=0,0≤t≤1,y′′′（t）＋f2（t,x（t）,y′（t）,y″（t））=0,0≤t≤1在适当的条件下解的存在性.
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| 关 键 词： | 三阶微分方程组 边值问题 Nagumo条件 上下解 拓扑度 |
The Existence of Solution of Muti-point Boundary Value Problem of a Class of Third-order Nonlinear Differential Systems |
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| XIE Chun,LUO Zhi-guo.The Existence of Solution of Muti-point Boundary Value Problem of a Class of Third-order Nonlinear Differential Systems[J].College Mathematics,2011,27(4):57-62. |
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| Authors: | XIE Chun LUO Zhi-guo |
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| Institution: | XIE Chun1,2,LUO Zhi-guo2(1.Department of Mathematics,Hunan Normal University,Changsha,410081,China,2.Department of Mathematics,Hunan Institute Of Humanities,Science And Technology,Loudi,417000,China) |
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| Abstract: | By applying degree theory and the lower and upper solutions method,it was obtained that in suitable conditions the existence of at least a solution to the third-order nonlinear differential systems as follow： {x′′′（t）＋f1（t,y（t）,x′（t）,x″（t））=0,0≤t≤1,y′′′（t）＋f2（t,x（t）,y′（t）,y″（t））=0,0≤t≤1. |
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| Keywords: | third-order differential system boundary value problem nagumo-type condition lower and upper solution topological degree |
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