| 高阶分数阶微分方程边值问题正解的存在性 |
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| 引用本文： | 刘东利,杨军,崔更新. 高阶分数阶微分方程边值问题正解的存在性[J]. 郑州大学学报(自然科学版), 2014, 0(1): 16-20 |
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| 作者姓名： | 刘东利 杨军 崔更新 |
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| 作者单位： | [1]燕山大学理学院,河北秦皇岛066004 [2]河北省数学研究所,河北石家庄050000 [3]北京理工大学数学学院,北京100081 |
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| 基金项目： | 国家自然科学基金资助项目,编号60604004;河北省应用基础研究计划重点基础研究项目,编号13961806D;秦皇岛市科技支撑计划项目,编号201001A037,201101A168. |
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| 摘 要： | 研究了一类非线性分数阶高阶微分方程边值问题正解的存在性,通过对相应分数阶Green函数的研究,并利用Banach不动点定理和Guo-Krasnosel＇skii不动点定理,得到方程存在唯一正解和至少存在一个正解的充分条件,最后给出一个例子来验证其中的主要结果.
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| 关 键 词： | 分数阶微分方程 Green函数 高阶 正解 不动点定理 |
Existence of Positive Solutions for Boundary Value Problem of Fractional High-order Differential Equations |
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| LIU Dong-li,YANG Jun,CUI Geng-xin. Existence of Positive Solutions for Boundary Value Problem of Fractional High-order Differential Equations[J]. Journal of Zhengzhou University (Natural Science), 2014, 0(1): 16-20 |
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| Authors: | LIU Dong-li YANG Jun CUI Geng-xin |
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| Affiliation: | 1. College of Science, Yanshan University, Qinhuangdao 066004, China; 2. Mathematics Research Center in Hebei Province, Shijiazhuang 050000, China ; 3. College of Science, Beijing Institute of Technology, Beijing 100081, China) |
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| Abstract: | The problem of the existence of positive solutions for a class of nonlinear fractional high-order differential equations with boundary value problem was studied. By studying the corresponding Green function, and using the Banach fixed point theorem and Guo-Krasnosel＇ skii fixed point theorem, some sufficient conditions were established for the existence of unique positive solution and at least one positive solutions. Further more, one example was presented to illustrate the main result. |
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| Keywords: | fractional differential equations Green function high-order positive solutions fixed pointtheorem |
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