一类具有p-Laplacian算子和积分边界条件的分数阶微分方程解的存在性

Existence of Solutions for a Class of Fractional Differential Equations with p-Laplacian Operators and Integral Boundary Conditions

研究了一类具有p-Laplacian算子和积分边界条件的分数阶微分方程解的存在性.当限定f(t,u(t))在两个不同区间上的范围以及满足"变异"的Lipschitz条件时,利用退化方程构造的Green函数及其性质,结合Guo-Krasnosel’skii不动点定理以及Banach压缩映射原理,分别证明了所研究问题的解的存在唯一性.

In this paper,we study the existence of solutions for a class of fractional differential equations with p-Laplacian operator and integral boundary conditions.When the range of on two different intervals is limited and the Lipschitz condition of"variation"is satisfied,the existence and uniqueness of the solution of the problem are proved by using the Green function and properties constructed by the degenerate equation,Guo-Krasnosel’skii fixed point theorem and Banach contraction mapping principle.