带p-Laplacian算子的分数阶微分方程共振无穷多点边值问题解的存在性  

Existence of solutions of fractional p-Laplacian differential equation with infinite-point boundary value conditions

作　　者：孔凡亮[1] 薛婷婷[1] 付丽娜[1] 陈星[1] KONG Fan-liang;XUE Ting-ting;FU Li-na;CHEN Xing(School of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023,China)

机构地区：[1]新疆工程学院数理学院,新疆乌鲁木齐830023

出　　处：《东北师大学报（自然科学版）》2022年第3期14-19,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(2021D01B35,2021D01A65);新疆维吾尔自治区高校科研项目(XJEDU2021Y048)。

摘　　要：讨论了一类具有p-Laplacian算子的分数阶微分方程共振无穷多点边值问题解的存在性,通过将分数阶p-Laplacian微分方程问题转换成等价的线性问题,利用Mawhin连续定理得到了方程至少存在一个解的充分条件,最后举例验证了结论的有效性.This paper is concerned with existence of solutions of infinite-point boundary value problems at resonance for fractional differential equations with p-Laplacian operator.Through transforming the fractional p-Laplacian problem into an equivalent linear problem, sufficient condition which guarantees the existence of at least one solution is obtained by using Mawhin continuation theorem.As an application, one example is presented to illustrate the result.

关 键 词：P-LAPLACIAN算子 无穷多点边值问题 正解 共振 

分 类 号：O175.8[理学—数学]