Hadamard型奇异非线性分数阶微分方程三点边值问题正解的存在唯一性

Existence and Uniqueness of Positive Solutions to Three-Point Boundary Value Problems for Singular Nonlinear Fractional Differential Equations of Hadamard Type

采用混合单调算子方法,研究了带有Hadamard型导数的奇异非线性分数阶微分方程三点边值问题正解的存在唯一性。将一般问题推广到了高阶的情况,构造了较为复杂的三元非线性项,得到了边值问题的可解性结果。

In this paper,the existence and uniqueness of positive solutions for three point boundary value problems of singular nonlinear fractional differential equations with Hadamard type derivatives are studied by using mixed monotone operator method.The general problem is extended to the case of higher order,a more complex ternary nonlinear term is constructed,and the solvability of the boundary value problem is obtained.