无穷区间上分数阶积分边值问题正解的存在唯一性  

Existence and uniqueness of positive solutions for fractional integral boundary value problems on the infinite interval

作　　者：郭晓珍 王文霞[1] GUO Xiaozhen;WANG Wenxia(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,Shanxi,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《华中师范大学学报（自然科学版）》2022年第5期752-757,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11361047).

摘　　要：该文研究一类无穷区间上带有积分边界条件和扰动参数的分数阶微分方程特征值问题.运用带参数的和算子不动点定理,建立了上述特征值问题存在唯一正解的最大特征值区间,并讨论了正解对参数的连续依赖性.特别地,给出了参数的临界值估计,最后,给出一个例子作为所获结果的应用.It is concerned with a class of eigenvalue problems of fractional differential equations with nonlinear integral boundary conditions and a disturbance parameter on the infinite interval in this paper.By using the fixed point theorem for a sum operator with a parameter,the maximum eigenvalue interval for the existence of the unique positive solution for the eigenvalue problem is established and it is showed that such a positive solution depends continuously on parameters.In particular,an estimate for the critical value of parameters is given.Finally,a example is given to illustrate our main results.

关 键 词：Riemann-Liouville分数阶导数 积分边值问题 参数 正解 

分 类 号：O175.8[理学—数学]