一类分数阶微分方程解和正解的存在性与唯一性  

The Existence and Uniqueness of Solutions and Positive Solutions for the Nonlinear Fractional Differential Equation

作　　者：胡雷[1] 王晓娟 张伟光[3] 

机构地区：[1]山东交通学院数理系,山东济南250023 [2]山东力明科技职业学院,山东济南250116 [3]济南中学,山东济南250001

出　　处：《淮阴师范学院学报（自然科学版）》2010年第1期19-25,共7页Journal of Huaiyin Teachers College;Natural Science Edition

摘　　要：研究了一类非线性分数次微分方程初值问题的解的存在性、唯一性以及正解的存在性,利用非线性Leray-Schauder不动点定理及Banach压缩映象原理得到了解的存在性和唯一性结论,利用锥压缩、锥拉伸定理获得了正解及多个正解的存在性.We investigate the existence of solution and positive solution to the nonlinear fractional differential equation. By Leary Shauder fixed point theorem, we obtain the existence of solution for the nonlinear fractional differential equation. By Banach fixed point theorem, we obtain the uniqueness of existence of solution for the equation. By the fixed point theorems of cone expansion and cone compression, we obtain the existence of positive solutions for the equation.

关 键 词：分数次导数 分数次微分方程 LERAY-SCHAUDER不动点定理 BANACH压缩映象原理 锥压缩 锥拉伸 

分 类 号：O175[理学—数学]