带p⁃Laplace算子的分数阶Langevin型方程对偶反周期边值问题解的存在唯一性  

Existence and uniqueness of solutions for fractional Langevin type equations with dual anti⁃periodic boundary conditions involving p⁃Laplace operator

作　　者：张纪凤 张伟 韦慧 倪晋波 ZHANG Ji-feng;ZHANG Wei;WEI Hui;NI Jin-bo(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,Anhui,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《山东大学学报（理学版）》2022年第9期91-100,共10页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11601007);安徽高校自然科学研究项目(KJ2020A0291);安徽理工大学研究生创新基金项目(2021CX2117)。

摘　　要：研究了一类新的分数阶Langevin型方程反周期边值问题。该方程带p⁃Laplace算子,边值条件由两对反周期边值条件构成(对偶反周期边值条件)。通过利用Krasnoselskii不动点定理以及Banach压缩映射定理分别得到了解的存在性与唯一性准则,并举例说明了主要结论,所得结果丰富了已有文献的相关工作。A new class of fractional Langevin type equations with anti⁃periodic boundary conditions is studied.The equations involve p⁃Laplace operator and the boundary conditions are constituted by two pairs of anti⁃periodic boundary conditions(dual anti⁃periodic boundary conditions).The criteria for the existence and uniqueness of solutions are presented by applying the Krasnoselskii's fixed point theorem and Banach contraction mapping principle,and two examples are constructed to support our main results.The results obtained in this study enrich the existing related works.

关 键 词：分数阶Langevin型方程 对偶反周期边值条件 p⁃Laplace算子 解存在唯一性 不动点定理 

分 类 号：O175.8[理学—数学]