Banach空间中带有Sturm-Liouville边界条件的分数阶微分方程解的存在性  

Existence of Solutions for Fractional Differential Equations with Sturm-Liouville Boundary Conditions in Banach Space

作　　者：宋学瑶 周文学[1] 吴亚斌 SONG Xueyao;ZHOU Wenxue;WU Yabin(College of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《武汉大学学报（理学版）》2022年第5期501-508,共8页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金(11961039,11801243);兰州交通大学校青年科学基金(2017012)

摘　　要：抽象空间微分方程的难点在于积分算子不再具有紧性,为了对相应的算子应用凝聚映射的不动点理论,通常要给非线性项添加非紧性条件。本文运用非紧性测度估计技巧、Sadovskii’s不动点定理和凝聚映射的Leray-Schauder不动点定理,研究了Banach空间中带有Sturm-Liouville边界条件的分数阶微分方程解的存在性,并举例说明所得结果的适用性。The difficulty of abstract space differential equation is that the integral operator is no longer compact.In order to apply the fixed point theorem of condensing mapping to the corresponding operator,it is usually necessary to add compactness conditions to the nonlinear term.In this paper,the existence of solutions for fractional differential equations with Sturm-Liouville boundary conditions in Banach space is investigated by using a new estimation technique for the measure of noncompactness,the Sadovskii’s fixed point theorem and the Leray-Schauder type fixed point theorem of condensing mapping.An example is given to show the applicability of main results.

关 键 词：一致分数阶导数 非紧性测度 Sadovskii’s不动点定理 LERAY-SCHAUDER不动点定理 

分 类 号：O175[理学—数学]