带p-Laplacian算子的半线性分数阶脉冲微分方程解的存在性与唯一性

Existence and uniqueness of solutions for semilinear fractional impulsive differential equation with p-Laplacian operator

研究了一类带p-Laplacian算子的半线性分数阶脉冲微分方程反周期边值问题.首先将分数阶微分方程转化为等价的积分方程,然后通过使用Schauder不动点定理、Schaefer不动点定理及Banach压缩映射原理得到了边值问题解的存在性与唯一性,最后举例验证主要结果的合理性.

We consider a class of anti-periodic boundary value problems of semilinear fractional impulsive differential equation with p-Laplacian operator.Firstly,the fractional differential equation is transfromed into equivalent integral equation.Secondly,we are devoted to the existence and uniqueness of solution for the boundary value problem by utilizing Schauder fixed-point theorem,Schaefer’s fixed-point theorem,and Banach compression mapping principle.Finally,examples are given to illustrate the main results.