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

作　　者：胡芳芳 胡卫敏 HU Fang-fang;HU Wei-min(College of Mathematics and Statistics,Yili Normal University,Yining 835000,China)

机构地区：[1]伊犁师范大学数学与统计分院,新疆伊宁835000

出　　处：《东北师大学报（自然科学版）》2020年第3期62-67,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：新疆维吾尔自治区自然科学基金资助项目(2019D01C331).

摘　　要：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.

关 键 词：P-LAPLACIAN算子 分数阶微分方程 不动点定理 正解 

分 类 号：O175.14[理学—数学]