临界点理论在分数阶微分方程边值问题中的应用  

Applications of Critical Point Theory to BoundaryValue Problems of Fractional Differential Equations

作　　者：秦锐珍 周文学[1] 曹美丽 QIN Ruizhen;ZHOU Wenxue;CAO Meili(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《吉林大学学报（理学版）》2024年第4期831-841,共11页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11961039)。

摘　　要：用临界点理论和变分法研究Banach空间中带Sturm-Liouville边值条件的Caputo型分数阶微分方程解的存在性.通过定义适当的分数阶导数空间,将分数阶微分方程边值问题解的存在性转化为寻找定义在某个空间上对应泛函的临界点,得到了该边值问题存在一系列无界的广义解.The critical point theory and the variational method were used to study the existence of the solution for the Caputo type fractional differential equation with the Sturm-Liouville boundary condition in Banach space.By defining the appropriate fractional derivative space,the existence of the solution to the boundary value problem of fractional differential equation was transformed into finding the critical point defined as the corresponding functional in a certain space,and a series of unbounded generalized solutions to the boundary value problem were obtained.

关 键 词：Sturm-Liouville边值条件 临界点理论 变分法 不连续分数阶导数 

分 类 号：O175.8[理学—数学]