一类Caputo型分数阶微分方程边值问题多正解的存在性  

Existence of Multiple Positive Solutions for a Class of Caputo Type Fractional Differential Equations Boundary Value Problems

作　　者：张敬凯 徐家发 柏仕坤 ZHANG Jingkai;XU Jiafa;BAI Shikun(College of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2022年第4期87-91,共5页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市自然科学基金(No.cstc2020jcyj-msxmX0123);重庆市教育委员会科技项目(No.KJQN202000528;No.KJQN201900539);重庆师范大学数学科学学院重点实验室开放课题(No.CSSXKFKTM202003)。

摘　　要：【目的】研究一类Caputo型分数阶微分方程边值问题。【方法】将该问题转化为等价的积分方程,构造相应的算子方程,在合适的工作空间中运用广义Avery-Henderson不动点定理研究该方程正解的存在性。【结果】该方程至少有3个正解。【结论】举例说明所得到的结论具有较广泛的适应性,推广和改进了已有的一些成果。[Purposes]Consider a class of Caputo type fractional differential equations boundary value problems.[Methods]It first translates the problem into its equivalent integral equation,establishes the corresponding operator equation,and then uses the generalized Avery-Henderson fixed point theorem to study the existence of positive solutions for the problem in an appropriate work space.[Findings]The equation has at least three positive solutions.[Conclusions]Finally,a specific example is given to illustrate that the conclusion has a wide application,and the result extends and generalizes the existing study in the literature.

关 键 词：Caputo型分数阶微分方程 边值问题 不动点定理 正解 

分 类 号：O175.1[理学—数学] O175.8[理学—基础数学]