| 完全三阶边值问题解的存在性 |
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| 引用本文： | 李菊鹏,李永祥.完全三阶边值问题解的存在性[J].四川大学学报(自然科学版),2018,55(4):688-692. |
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| 作者姓名： | 李菊鹏 李永祥 |
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| 作者单位： | 西北师范大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金(11261053,11661071) |
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| 摘 要： | 本文讨论了如下完全三阶两点边值问题{-u(t)=f(t,u(t),u′(t),u″(t)),t∈0,1],u(0)=u′(0)=u″(1)=0解的存在性,其中f:0,1]×R3→R为连续函数.当f(t,x,y,z)满足关于x,y,z超线性增长的不等式条件及f(t,x,y,z)关于z满足Nagumo型增长条件时,本文应用Leray-Schauder不动点定理获得了该问题解的存在性.
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| 关 键 词： | 完全三阶边值问题 超线性增长 Nagumo型增长条件 Leray-schauder不动点定理 |
| 收稿时间： | 2017/11/15 0:00:00 |
| 修稿时间： | 2017/12/8 0:00:00 |
Existence of solutions of a third-order boundary value problem |
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| LI Ju-Peng and LI Yong-Xiang.Existence of solutions of a third-order boundary value problem[J].Journal of Sichuan University (Natural Science Edition),2018,55(4):688-692. |
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| Authors: | LI Ju-Peng and LI Yong-Xiang |
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| Institution: | College of Mathematics and Statistics, Northwest Normal University and College of Mathematics and Statistics, Northwest Normal University |
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| Abstract: | In this paper,the existence of solutions of a class of fully third order boundary value problem is considered, where f is continuous. Applying the Leray-schauder fixed point theorem, the existence of solutions is obtained under f satisfies an inequality condition that allows f superlinear growth and f satisfies the Nagumo-type growth condition on z. |
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| Keywords: | Fully three order boundary value problem Superlinear growth Nagumo-type growth condition Leray-schauder fixed point theorem |
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