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| 非线性分数微分方程边值问题正解的存在性(英文) | |
| 引用本文： | 宋利梅,翁佩查. 非线性分数微分方程边值问题正解的存在性(英文)[J]. 数学季刊, 2012, 0(2): 293-300 |
| 作者姓名： | 宋利梅 翁佩查 |
| 作者单位： | School of Mathematics,Jiaying University;School of Mathematical Science,South China Normal University |
| 基金项目： | Supported by the Research Fund for the Doctoral Program of High Education of China(20094407110001);Supported by the NSF of Guangdong Province(10151063101000003) |
| 摘 要： | In this paper,we study a Dirichlet-type boundary value problem（BVP） of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative Dαo+is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel’skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results. |
| 关 键 词： | fractional differential equation boundary value problem positive solution fractional Green function fixed-point theorem in cones |
Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Differential Equation |
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| Affiliation: | SONG Li-mei1,WENG Pei-xuan2(1.School of Mathematics,Jiaying University,Meizhou 514015,China;2.School of Mathematical Science,South China Normal University,Guangzhou 510631,China) |
| Abstract: | In this paper,we study a Dirichlet-type boundary value problem（BVP） of nonlinear fractional differential equation with an order α ∈(3,4],where the fractional derivative Dαo+ is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel’skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results. |
| Keywords: | fractional differential equation boundary value problem positive solution fractional Green function fixed-point theorem in cones |
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