分数阶微分方程积分边值问题正解存在性  

Existence of positive solutions of fractional differential equations with integral boundary value conditions

作　　者：李金晓[1] 杨军[1] 李亚[1] 刘东利[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第1期132-136,共5页Journal of Liaoning Technical University (Natural Science)

摘　　要：为考察一类非线性分数阶微分方程在积分边界条件下正解的存在性,利用格林函数和Guo-Krasnoselskii不动点定理,研究了分数阶微分方程积分边值问题的正解,并得到了积分边值问题至少存在一个正解的判别准则.结果表明:这类分数阶微分方程边值问题的正解具有存在性,所得的结论丰富了分数阶微分方程正解的存在性的研究成果.In order to investigate the existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions, this paper discussed the positive solutions of integral boundary value problems using Green functions and Guo-Krasnoselski fixed point theorem, and derived at least one positive solution for integral boundary value problems. The results of this paper show that the class of nonlinear fractional differential equations with integral boundary conditions possess existence, and the conclusion enrich the research findings for existence of positive solutions of fractional differential equations.

关 键 词：分数阶微分方程 正解 格林函数 积分边值问题 存在性 不动点定理 锥 等度连续 

分 类 号：O175.8[理学—数学]