一类无穷区间上的分数阶微分方程边值问题解的存在性
The Existence of Solutions for a Class of Boundary Value Problem of Fractional Differential Equations on an Infinite Interval
DOI: 10.12677/PM.2017.74027, PDF, HTML, XML, 下载: 1,627  浏览: 7,025  国家自然科学基金支持
作者: 姚佳欣*, 王文霞*, 贾建梅*：太原师范学院数学系，山西 晋中
关键词: 分数阶微分方程；积分边值问题；无穷区间；正解；Fractional Differential Equations； Integral Boundary Conditions； Infinite Interval； Positive Solutions
摘要: 利用Leray-Schauder非线性抉择定理以及Leggett-Williams不动点定理研究了一类无穷区间上的分数阶微分方程积分边值问题，获得了该边值问题至少存在一个无界解和三个正解的充分条件。最后给出了两个例子作为所获结果的应用。
Abstract: By using the Leray-Schauder nonlinear alternative theorem and the Leggett-Williams fixed point theorem, a class of boundary value problem for fractional differential equations with integral conditions on an infinite interval is investigated. Some sufficient conditions on the existence of at least one unbounded solution and three positive solutions are established. At last, two examples are given to illustrate the results.
文章引用：姚佳欣, 王文霞, 贾建梅. 一类无穷区间上的分数阶微分方程边值问题解的存在性[J]. 理论数学, 2017, 7(4): 213-224. https://doi.org/10.12677/PM.2017.74027

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