| 一类分数阶微分方程积分边值问题正解的分歧性 |
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| 引用本文： | 孔祥山,李海涛,赵洪欣,吕寻景.一类分数阶微分方程积分边值问题正解的分歧性[J].高校应用数学学报(A辑),2017,32(1). |
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| 作者姓名： | 孔祥山 李海涛 赵洪欣 吕寻景 |
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| 作者单位： | 1. 青岛滨海学院大专文理基础学院,山东青岛,266555;2. 山东师范大学数学与统计学院,山东济南,250014 |
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| 基金项目： | 国家自然科学基金，山东省自然科学基金，山东省自然科学杰出青年基金 |
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| 摘 要： | 利用分歧方法和拓扑度理论,研究了一类带参数的分数阶微分方程积分边值问题正解的存在性.根据格林函数的性质,得到了系统正解的存在的若干充分条件.最后,通过数值例子验证了所得结果的有效性.
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| 关 键 词： | Riemann-Liouville分数阶微分方程 积分边值问题 分歧方法 正解 |
Bifurcation of positive solutions for a class of integral boundary value problems of fractional differential equations |
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| KONG Xiang-shan,LI Hai-tao,ZHAO Hong-xin,LV Xun-jing.Bifurcation of positive solutions for a class of integral boundary value problems of fractional differential equations[J].Applied Mathematics A Journal of Chinese Universities,2017,32(1). |
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| Authors: | KONG Xiang-shan LI Hai-tao ZHAO Hong-xin LV Xun-jing |
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| Abstract: | Using bifurcation techniques and topological degree theory, this paper investigates the existence of positive solutions for a class of integral boundary value problems of fractional differential equations. Based on the property of the Green function, several sufficient conditions are presented for the existence of positive solutions. Finally, the study of an illustrative example shows that the obtained results are effective. |
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| Keywords: | Riemann-Liouville fractional differential equation integral boundary value problem bifurcation technique positive solution |
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