| 非线性分数阶Dirichlet型边值正解的存在唯一性 |
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| 引用本文： | 古传运.非线性分数阶Dirichlet型边值正解的存在唯一性[J].四川理工学院学报(自然科学版),2014(3):94-97. |
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| 作者姓名： | 古传运 |
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| 作者单位： | 四川文理学院数学与财经学院,四川达州635000 |
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| 基金项目： | 四川省教育厅项目（14ZB0309） |
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| 摘 要： | 研究了一类非线性分数阶Dirichlet型边值问题。使用广义的凸算子的不动点定理与Green函数的性质和在一定的条件下,得到此边值问题正解的存在唯一性,并能构造一迭代序列去逼近此解。正解的存在性结论得到完善和推广。
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| 关 键 词： | 边值问题 广义的凸算子 不动点 正解 存在唯一性 |
Existence-uniqueness of Positive Solutions for Nonlinear Fractional Dirichlet-type Boundary Values |
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| GU Chuanyun.Existence-uniqueness of Positive Solutions for Nonlinear Fractional Dirichlet-type Boundary Values[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2014(3):94-97. |
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| Authors: | GU Chuanyun |
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| Institution: | GU Chuanyun (College of Mathematics and Finance-Economics, Sichuan University of Arts and Science, Dazhou 635000, China) |
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| Abstract: | This work is concerned with a class of the nonlinear fractional Dirichlet-type boundary value problem. By using the fixed point theorems of generalized convex operators and the properties of the Green function,the existence-uniqueness of positive solutions of this boundary value problem is obtained under certain conditions,and an iterative scheme is constructed to approximate this solution. The existence theory of positive solution is completed and generalized. |
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| Keywords: | boundary value problem generalized convex operators fixed point positive solution existence and uniqueness |
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