具p-Laplacian算子的分数阶微分方程边值问题的多重正解

Multiple positive solutions for boundary value problems of fractional differential equations with p-Laplacian operator

研究了一类具有p-Laplacian算子的分数阶微分方程边值问题的多重正解.首先给出了格林函数及其性质,其次将边值问题转化为与其等价的积分方程,最后利用锥压缩锥拉伸不动点定理和Leggett-Williams不动点定理分别证明了边值问题一个及多个正解的存在性,并给出实例加以验证.

The multiple positive solutions for a class of boundary value problems of fractional differential equations with p-Laplacian operator are studied.By using the cone compression cone stretching fixed point theorem and the Leggett-Williams fixed point theorem respectively,the existence of one or more positive solutions of the boundary value problem is given.