具p-Laplacian算子的半正分数阶脉冲微分方程三点边值问题解的存在性与唯一性  

The existence and uniqueness of solutions for semipositive impulsive fractional differential equation to three-point boundary value problems with p-Laplacian operator

作　　者：盛世昌 张婷婷 胡卫敏 SHENG Shichang;ZHANG Tinging;HU Weimin(School of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China;Institute of Applied Mathematics,Yili Normal University,Yining 835000,Xinjiang,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《华中师范大学学报（自然科学版）》2023年第5期696-703,共8页Journal of Central China Normal University：Natural Sciences

基　　金：新疆维吾尔自治区自然科学基金项目(2019D01C331);伊犁师范大学高级别培育项目(YSPY2022014);伊犁师范大学科研创新团队培育计划项目(CXZK2021016)。

摘　　要：该文基于Caputo分数阶微分方程,讨论了一个具p-Laplacian算子的半正分数阶微分方程三点脉冲边值问题解的存在性,主要是利用Banach不动点定理和Schauder不动点定理证明了解的存在性.其主要方法是先找出分数阶脉冲微分方程等价的积分方程,然后构造映射,再运用不动点定理,获得方程解的存在性及唯一性的充分条件.文章最后举例说明了主要结果的应用.In this paper,based on Caputo fractional differential equation,the existence of solutions for a semi-positive fractional differential equation with p-Laplacian operator is discussed.Banach fixed point theorem and Schauder fixed point theorem are used to prove the existence of solutions.The main method is to find the integral equation equivalent to fractional impulsive differential equation,construct the mapping,and use the fixed point theorem to obtain sufficient conditions for the existence and uniqueness of the solution of the equation.Finally,an example is given to illustrate the application of the main results.

关 键 词：脉冲 P-LAPLACIAN算子 分数阶微分方程 三点边值问题 

分 类 号：O175.8[理学—数学]