分数阶微分方程多点边值问题的正解

Multiple Positive Solutions for Multi-Point Boundary Value Problem of Fractional Differential Equation

中文关键词:  分数阶微分方程  多点边值问题  正解  Green函数  不动点定理

英文关键词:fractional differential equation  multi-point boundary value problem  positive solution  Green function  fixed point theorem

中文摘要:

      本文研究了在边界条件中含有多个分数导数项的分数阶微分方程多点边值问题多个正解的存在性.运用Green函数的性质以及有白-葛推导出的一般形式的Leggett-Williams不动点定理,建立了边值问题至少有三个正解存在的充分条件.最后,给出了一个例子,用于说明所得主要结论具有广泛的适用性.

英文摘要:

      In this paper, we study the multiplicity of positive solutions for multi-point boundary value problem of Riemann-Liouville fractional differential equation with multi-terms fractional derivative in the boundary conditions. By using the properties of the Green function and a generalization of the Leggett-Williams fixed point theorem due to the work of Bai and Ge, the sufficient conditions to guarantee the existence of at least three positive solutions are established. In the end of this paper, we have also given out the example to illustrate the wide range of potential application of our main results.