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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (1): 13-22    
    
一类分数阶微分方程积分边值问题正解的分歧性
孔祥山1, 李海涛2, 赵洪欣1, 吕寻景1
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
Bifurcation of positive solutions for a class of integral boundary value problems of fractional differential equations
KONG Xiang-shan1, LI Hai-tao2 , ZHAO Hong-xin1 , LV Xun-jing1
1. Basic Science Department, Qingdao Binhai University, Qingdao 266555, China
2. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
 全文: PDF 
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.
关键词： Riemann-Liouville分数阶微分方程;  积分边值问题;  分歧方法;  正解    
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.
Key words:  Riemann-Liouville fractional differential equation    integral boundary value problem    bifurcation technique    positive solution
收稿日期: 2016-09-03 出版日期: 2018-03-18
:  O175.6  
基金资助: 国家自然科学基金(61503225); 山东省自然科学基金(ZR2015FQ003); 山东省自然科学杰出青年基金(JQ201613)
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孔祥山
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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, 2017, 32(1): 13-22.

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. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 13-22.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I1/13

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