| 奇异分数微分方程耦合系统边值问题的正解(英文) |
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| 引用本文： | 宋利梅.奇异分数微分方程耦合系统边值问题的正解(英文)[J].安徽师范大学学报(自然科学版),2011,34(4):307-313. |
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| 作者姓名： | 宋利梅 |
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| 作者单位： | 嘉应学院数学学院,广东梅州,514015 |
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| 基金项目： | Supported by the Natural Science Foundation of Guangdong Province(10151063101000003) |
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| 摘 要： | 研究一类Dirichlet型非线性α,β∈(3,4]阶奇异分数微分方程耦合系统边值问题,其中分数导数D0α+,D0β+是标准的Riemann-Liouville分数导数.利用锥上Krasnosel’skii不动点定理和Leray-Schauder非线性二择一定理,得到该边值问题正解存在的若干准则.文中还举例说明了所得结果的可应用性.
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| 关 键 词： | 奇异耦合系统 分数微分方程 边值问题 正解 锥上不动点定理 |
Positive Solution to Boundary Value Problem for a Singular Coupled System of Fractional Differential Equations |
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| SONG Li-mei.Positive Solution to Boundary Value Problem for a Singular Coupled System of Fractional Differential Equations[J].Journal of Anhui Normal University(Natural Science Edition),2011,34(4):307-313. |
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| Authors: | SONG Li-mei |
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| Institution: | SONG Li-mei(School of Mathematics,Jiaying University,Meizhou 514015,China) |
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| Abstract: | In this paper,we study a Dirichlet-type boundary value problem (BVP) of nonlinearfractional differential equation with an order α,β ∈ (3,4],where the fractional derivativeDα0+,Dβ0+ isthe standard Riemann-Liouville fractinal derivative.By means of the Leray-Schauder nonlinearalternative and Krasnosel' skii fixed-point theorem in cones,we obtain some criteria for the existence ofone positive solution for the above BVP.We also give examples to illustrate the applicability of ourresults. |
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| Keywords: | singular coupled system fractional differential equation boundary value problem positivesolution fixed-point theorem in cones |
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