分数阶p-Laplacian脉冲微分方程边值问题解的存在性与唯一性

The Existence and Uniqueness of Solutions for the Boundary Value Problem of Fractional Impulsive Difference Equation with p-Laplacian Operator

研究了一类分数阶p-Laplacian脉冲微分方程边值问题解的存在性与唯一性.首先根据已知条件得到了问题的Green函数,然后将脉冲问题转化为等价的积分方程,最后利用Leray-Schauder不动点定理和Banach压缩映像原理给出解存在性和唯一性的充分条件,并通过实例加以验证.

This paper,we discuss the existence and uniqueness of solutions for the boundary value problem of impulsive fractional differential equations with p-Laplacian operator.Firstly,Green’s function is obtained according to the known conditions,and then the impulse problem is transformed into an equivalent integral equation.The sufficient conditions for the existence and uniqueness of the solution of the differential equation are given by using the Leary-Schauder fixed point theorem and the Banach principle of compressed image,and the method could be tested and verified with living example.