一类无穷域上分数阶微分方程正解存在性  

Existence of a fractional differential equations infinite domain

作　　者：李亚[1] 杨军[1] 刘东利[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066000

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第1期112-115,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(60604004);河北省自然科学基金资助项目(07M005)

摘　　要：针对无穷域上非线性半正高阶分数阶微分方程多点边值问题正解的存在问题,采用Schauder不动点定理以及迭代的方法,研究该方程正解的存在性,给出了正解的存在条件.结果表明:对于无穷域上非线性半正高阶分数阶微分方程多点边值问题正解的存在性的证明,不需要使用复杂的对角化过程,即可得出结论,方法比以往更一般化、简单化.In order to solve the problem of nonlinear semipositone high-order fractional differential equations of multi-point boundary value problems of the existence of positive solutions, using Schauder fixed point theorem and iteration method, this paper researched the existence of positive solutions of the equation, and specified the condition for the existence of positive solutions. The results show that without using the complex diagonalization process, it can prove the nonlinear semipositone high-order fractional differential equations of multi-point bounctary value problems of the existence of positive solution. This method is more general and simplified.

关 键 词：分数阶 微分方程 无穷域 边值问题 SCHAUDER不动点定理 迭代法 正解 存在性 

分 类 号：O175.8[理学—数学]