抽象空间中Hadamard分数阶微分方程奇异边值问题正解的存在性

Existence of positive solutions for singular boundary value problems of Hadamard fractional differential equations in abstract space

研究了Banach空间中奇异边值问题正解的存在性。通过构造一个特殊的锥,利用严格集压缩算子的不动点指数理论,建立了该边值问题的近似问题至少有两个正解的存在性。然后借助Ascoli-Arzela定理,利用近似问题解序列的相对紧性,得到边值问题至少有两个正解的充分条件。

The existence of positive solutions of singular boundary value problems in Banach space is investigated.By constructing a new cone and using the fixed point index theory of strict set compression operator,it is established that there are at least two positive solutions for the corresponding approximation of the boundary value problem.Then,using Ascoli-Arzela theorem and the relative compactness of the sequence of solutions,a sufficient condition is obtained for the existence of multiple positive solutions to boundary value problem.