带p—Laplacian算子的分数阶微分方程多点边值问题的解的存在性

吕秋燕++刘文斌++唐敏++申腾飞++程玲玲

摘 要 利用不动点定理，研究带有p-Laplacian算子的分数阶微分方程多点边值问题解的存在性，得到边值问题至少存在一个解的充分条件.

关键词 分数阶微分方程；p-Laplacian算子；存在性；不动点定理

中图分类号 O175.8 文献标识码 A 文章编号 10002537（2016）01008005

Exitence of Solutions for Fractions Multipoint

Boundary Value Problem with p-Laplacian Operator

LV Qiuyan1， LIU Wenbin2*， TANG Min2， SHEN Tengfei2， CHENG Lingling2

（1.Dongshan High School， Suzhou 215107， China；

2.College of Science， China University of Mining and Technology， Xuzhou 221116， China）

Abstract

This paper presents a study on the existence of solutions for the fractional multi-point boundary value problem with p-Laplacian operator. Making use of the fixed-point theorem， we obtained sufficient conditions to guarantee the existence of at least one solution for the boundary value problem.

Key words fractional differential equation； p-Laplacian operator； existence； fixed point theorem

显然，问题（4）满足定理2.1的假设条件.因此，至少存在一个解.

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（编辑 HWJ）