| 二阶非线性积分边值问题正解的存在唯一性 |
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| 引用本文： | 蔡蕙泽,韩晓玲. 二阶非线性积分边值问题正解的存在唯一性[J]. 四川大学学报(自然科学版), 2019, 56(3): 399-403 |
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| 作者姓名： | 蔡蕙泽 韩晓玲 |
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| 作者单位： | 西北师范大学数学与统计学院,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(11561063) |
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| 摘 要： | 本文运用双度量空间中的广义Krasnoselskii’s压缩不动点定理研究了二阶非线性积分边值问题u″+a(t)f(t,u(t),u′(t))=0,t∈(0,1),u(0)=0,u(1)=α∫~η_0u(s)ds正解的存在唯一性,其中■:[0,1]×[0,∞)×R→[0,∞)连续,且当t_0∈[η,1]时a(t_0)0.
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| 关 键 词： | 正解；存在唯一性；积分边值问题 广义压缩不动点定理 |
| 收稿时间： | 2018-07-02 |
| 修稿时间： | 2018-10-12 |
Existence and uniqueness of positive solutions for second-order nonlinear integral boundary value problem |
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| Cai Hui-Ze and Han Xiao-Ling. Existence and uniqueness of positive solutions for second-order nonlinear integral boundary value problem[J]. Journal of Sichuan University (Natural Science Edition), 2019, 56(3): 399-403 |
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| Authors: | Cai Hui-Ze and Han Xiao-Ling |
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| Affiliation: | 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,by using the method of generalized Krasnoselskii''s contractive fixed point theorem in bimetric spaces we study the existence and uniqueness of the positive solutions for the following second-order nonlinear integral boundary value problem$$u''+a(t)f(t,u(t),u''(t))=0,~tin(0,1),$$$$u(0)=0,~alphaint_{0}^{eta}u(s)ds=u(1),$$where$~00,~$and$~f:[0,1]times[0,infty)times Rrightarrow[0,infty)~$is continuous. |
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| Keywords: | Positive solution Existence and uniqueness Integral boundary value problem Generalized contractive fixed point theorem |
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