|
|||||
|
|
| 一类分数阶微分方程解和正解的存在性与唯一性 | |
| 引用本文： | 胡雷,王晓娟,张伟光.一类分数阶微分方程解和正解的存在性与唯一性[J].淮阴师范学院学报(自然科学版),2010,9(1):19-25. |
| 作者姓名： | 胡雷 王晓娟 张伟光 |
| 作者单位： | 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 |
| 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. |
| 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 |
The Existence and Uniqueness of Solutions and Positive Solutions for the Nonlinear Fractional Differential Equation |
|
| HU Lei,WANG Xiao-juan,ZHANG Wei-guang.The Existence and Uniqueness of Solutions and Positive Solutions for the Nonlinear Fractional Differential Equation[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2010,9(1):19-25. | |
| Authors: | HU Lei WANG Xiao-juan ZHANG Wei-guang |
| Institution: | 1.Department of Mathematics & Physics;Shandong JiaoTong University;Shandong Jinan 250023;China;2.Department of Basic Subject;Shandong Liming Technology University;Shandong Jinan 250116;China;3.Jinan High School;Shandong Jinan 250001;China |
| Abstract: | 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. |
| Keywords: | fractional derivative fractional differential equation Leary Shauder fixed point theorem tcone expansion cone compression Banach's contraction theorem |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |