基于复合非线性算子不动点定理的分数阶多点边值问题研究  

Research on Fractional Multipoint Boundary Value Problems Based on the Fixed Point Theorem of Composition Nonlinear Operators

作　　者：张楠 张玲玲 刘宏伟 王慧 ZHANG Nan;ZHANG Lingling;LIU Hongwei;WANG Hui(Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《山西大学学报（自然科学版）》2024年第4期691-698,共8页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省回国留学人员科研资助项目(2021-030);山西省青年科学研究项目(202103021223060)。

摘　　要：本文研究了一类分数阶多点边值问题解的存在唯一性。首先考虑了一类复合型非线性算子,根据算子不同的性质,给出相应的算子不动点定理,由此获得了该方程存在唯一解的若干充分条件。作为应用,通过具体例子做了进一步的阐述。This article investigates the existence and uniqueness of solutions to a class of fractional multipoint boundary value problems.Firstly,we consider a class of composition nonlinear operator and provide corresponding fixed point theorems based on different properties of the operators.Then,several sufficient conditions for existence and uniqueness of solutions to the equation are obtained.As an application,an example is presented to illustrate the main results.

关 键 词：不动点 锥与半序 混合单调算子 分数阶微分方程边值问题 解的存在唯一性 

分 类 号：O175[理学—数学]