一类分数阶奇异微分方程边值问题正解的存在性

The Existence of Positive Solutions for the Boundary Value Problem of a Singular Fractional Differential Equation

给出了一类Riemann-Liouville微分方程边值问题的Green函数,进而得到了分数阶微分方程解的基本形式.将方程右边函数做适当修改,使之连续并满足一定条件,利用锥上的Krasnoselskii's不动点定理和Leray-Schauder选择定理,证明了这类方程在边界条件下至少有一个和两个正解存在的充分条件.

A class of Riemann-Liouville differential equation Green＇s function under boundary value problems were introduced, from which the basic form of the solutions of fractional differential equation was got. The right side of the equation was made appropriate changes, which is made continuously and certain conditions were satisfied, Krasnoselskii＇ s fixed point theorem and Leray-Schauder selection theorem were used, it is proved that sufficient conditions of at least one and two positive solutions of the equation exists under boundary conditions.