一类Caputo型分数阶微分方程边值问题多重正解存在的充分条件  

Sufficient conditions for the existence of multiple positive solutions for a Caputo type fractional-order differential equation boundary value problems

作　　者：于洋 葛琦[1] YU Yang;GE Qi(College of Science,Yanbian University,Yanji 133002,China)

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《延边大学学报（自然科学版）》2023年第2期95-101,共7页Journal of Yanbian University（Natural Science Edition）

基　　金：吉林省教育厅科学技术研究项目(JJKH2022527KJ)。

摘　　要：研究了一类非线性项带有分数阶导数的Caputo型分数阶微分方程的边值问题.首先,将方程转化为等价的积分方程;其次,通过计算得到了与该方程相应的格林函数,并且分析了所得的格林函数的性质;最后,利用格林函数的性质以及Guo-Krasnosel’skii不动点定理和Leggett-Williams不动点定理得到了该边值问题分别存在1个正解和3个正解的充分条件.The boundary value problems of Caputo type fractional differential equations with nonlinear terms and fractional derivatives were studied.Firstly,the equation was transformed into an equivalent integral equation.Secondly,Green function corresponding to the equation was obtained through calculation,and the properties of the obtained Green function were analyzed.Finally,by using the properties of Green function and the Guo-Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem,the sufficient conditions for the existence of one positive solution and three positive solutions for the boundary value problems were obtained.

关 键 词：Caputo型分数阶微分方程 格林函数 Guo-Krasnosel’skii不动点定理 LEGGETT-WILLIAMS不动点定理 边值问题 多重正解 

分 类 号：O175.8[理学—数学]