分数微分方程边值问题正解的存在与不存在性

Existence and Nonexistence of Positive Solutions for Boundary Value Problem of a Fractional Differential Equation

对一类含参变量的非线性Riemann-Liouville分数阶微分方程进行了研究,主要利用的工具是锥拉伸与锥压缩不动点理论,通过对问题中参数取值范围的讨论,得到了该问题正解存在与不存在的条件。非线性项中含有未知函数的分数阶导数,推广了相应的结果。

A class of nonlinear fractional differential equation concerning parameters was studied.The main methods used was the fixed-point theory on cone expansion and compression.Some conditions of existence and nonexistence of positive solutions were established.The polynomial expression contained the fractional derivative of unknown function,so a general result was obtained.