分数阶微分方程无穷多点边值问题的正解
Positive Solutions for Infinite-Point Boundary Value Problems of Fractional Differential Equations
摘要: 本文研究了带有积分边界条件的分数阶微分方程无穷多点边值问题的正解。该边值问题正解的存在性是通过Green函数的性质和不动点定理获得的。首先求出非线性系统对于线性系统的Green函数，之后给出Green函数的性质并构造合适的积分算子，然后通过使用不动点定理得到边值问题正解的存在性结果。最后，本文给出具体实例来说明得到定理的实用性。
Abstract: This paper studies the positive solutions of the infinite-point boundary value problem for fractional differential equations with integral boundary conditions. The existence of positive solutions for boundary value problems is obtained through the properties of Green’s function and the fixed point theorem. Firstly, Green’s function for the nonlinear system relative to the linear system is derived. Then, the properties of the Green’s function are presented and a suitable integral operator is constructed. Finally, the existence results of positive solutions for the boundary value problem are obtained by using the fixed point theorem. At the end, specific example is provided to illustrate the practicality of the obtained theorems.
文章引用：王梦真. 分数阶微分方程无穷多点边值问题的正解[J]. 应用数学进展, 2025, 14(6): 64-78. https://doi.org/10.12677/aam.2025.146301

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