带p-Laplacian算子的分数阶微分方程边值问题正解的存在性与多重性  

Existence and Multiplicity of Positive Solutions to Boundary Value Problems of Fractional Differential Equations with p-Laplacian Operator

作　　者：周文学[1] 吴亚斌 宋学瑶 ZHOU Wenxue;WU Yabin;SONG Xueyao(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《应用数学》2023年第4期997-1006,共10页Mathematica Applicata

基　　金：国家自然科学基金(11961039,11801243);兰州交通大学校青年科学基金(2017012)。

摘　　要：本文讨论一类带有p-Laplacian算子的一致分数阶微分方程边值问题正解的存在性.首先构造出相应的Green函数,将边值问题转化为等价的积分方程.然后通过Green函数相关性质、Guo-Krasnosel’skii不动点定理、Leggett-Williams不动点定理和单调迭代技巧建立了边值问题正解的存在性与多重性结论.最后举例验证主要结果的适用性.The existence of positive solutions to the boundary value problem of conformable fractional differential equations with p-Laplacian operator is discussed.First of all,the corresponding Green function is constructed and the boundary value problem is transformed into equivalent integral equation.Then,by applying related properties of the Green function,Guo-Krasnosel’skii fixed point theorem,Leggett-Williams fixed point theorem and monotone iterative technique,the existence and multiplicity conclusion of positive solutions of the boundary problem are established.Finally,some examples are included to illustrate the main results.

关 键 词：分数阶微分方程 边值问题 GREEN函数 不动点定理 单调迭代技巧 

分 类 号：O175.8[理学—数学]