一类带有p-Laplacian算子的分数阶微分方程边值问题的多重正解  

Multiple Positive Solutions of Boundary Value Problems for a Class of Fractional Differential Equations with p-Laplacian Operators

作　　者：胡芳芳 刘元彬 张永 HU Fangfang;LIU Yuanbin;ZHANG Yong(School of Mathematics and Statistics,Yili Normal University,Yining Xinjiang 835000,China;Institute of Applied Mathematics,Yili Normal University,Yining Xinjiang 835000,China;College of Mathematics and Physics,Xinjiang Institute of Technology,Changji Xinjiang 830091,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000 [3]新疆工程学院数理学院,新疆昌吉830091

出　　处：《西南师范大学学报（自然科学版）》2022年第11期31-40,共10页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：伊犁师范大学校级项目(2021YSYB075).

摘　　要：研究了一类带有p-Laplacian算子的Riemann-Liouville分数阶微分方程边值问题正解的存在性.在适当的边值条件下,首先运用积分变换和拉普拉斯变换将原来的边值问题转化为与其等价的积分方程,其次利用锥压缩、锥拉伸不动点定理和Leggett-Williams不动点定理分别证明边值问题一个及多个正解的存在性,最后通过算例验证主要结论的有效性,推广和改进了相关结论.The existence of positive solutions for a class of Riemann-Liouville boundary value problems for fractional differential equations with p-Laplacian operators has been studied.Under the appropriate boundary value conditions,the original boundary value problems are transformed into their equivalent integral equations by means of integral transform and Laplace transform.Secondly,the cone-compression cone-stretch fixed point theorem and Leggett-Williams fixed point theorem are used to prove the existence of one or more positive solutions to the boundary value problem.Finally,the validity of the main conclusions is verified by a numerical example,and the relevant conclusions are extended and improved.

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]