| 分数微分方程边值问题正解的存在与不存在性 |
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| 引用本文： | 李瑞瑞,刘文斌.分数微分方程边值问题正解的存在与不存在性[J].河南科技大学学报(自然科学版),2011,32(2):75-78,82,112. |
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| 作者姓名： | 李瑞瑞 刘文斌 |
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| 作者单位： | 中国矿业大学理学院,江苏徐州,221116 |
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| 基金项目： | 国家自然科学基金项目(10771212) |
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| 摘 要： | 对一类含参变量的非线性Riemann-Liouville分数阶微分方程进行了研究,主要利用的工具是锥拉伸与锥压缩不动点理论,通过对问题中参数取值范围的讨论,得到了该问题正解存在与不存在的条件。非线性项中含有未知函数的分数阶导数,推广了相应的结果。
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| 关 键 词： | 分数阶边值问题 正解 Krasnoesel’skii’s不动点 |
Existence and Nonexistence of Positive Solutions for Boundary Value Problem of a Fractional Differential Equation |
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| LI Rui-Rui,LIU Wen-Bin.Existence and Nonexistence of Positive Solutions for Boundary Value Problem of a Fractional Differential Equation[J].Journal of Henan University of Science & Technology:Natural Science,2011,32(2):75-78,82,112. |
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| Authors: | LI Rui-Rui LIU Wen-Bin |
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| Institution: | LI Rui-Rui,LIU Wen-Bin (College of Science,China University of Mining & Technology,Xuzhou 221116,China) |
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| Abstract: | A class of nonlinear fractional differential equation concerning parameters was studied.The main methods used was the fixed-point theory on cone expansion and compression.Some conditions of existence and nonexistence of positive solutions were established.The polynomial expression contained the fractional derivative of unknown function,so a general result was obtained. |
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| Keywords: | Fractional boundary value problem Positive solutions Krasnoesel′skii′s fixed-point theory |
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