一类具有p-Laplacian算子和积分边界条件的分数阶微分方程解的存在性  

Existence of Solutions for a Class of Fractional Differential Equations with p-Laplacian Operators and Integral Boundary Conditions

作　　者：许佰雁[1,2] 姜亦成 田纪亚[4] XU Bai-yan;JIANG Yi-cheng;TIAN Ji-ya(Basic Research Section,Changchun Guanghua University,Changchun 130033,China;Department of Science,Xinjiang Institute of Technology,Aksu 843100,China;College of Science,Qiqihar University,Qiqihaer 161006,China;School of Electrical Information,Changchun Guanghua University,Changchun 130033,China)

机构地区：[1]长春光华学院基础教研部,吉林长春130033 [2]新疆理工大学理学系,新疆阿克苏843100 [3]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006 [4]长春光华学院电气信息学院,吉林长春130033

出　　处：《数学的实践与认识》2020年第15期177-183,共7页Mathematics in Practice and Theory

基　　金：吉林省教育厅“十三五”科学技术项目(No.JJKH20171027KJ);吉林省发改委基金(2019C054-7);长春光华学院青年科研重点基金项目(QNJJZD2019005)。

摘　　要：研究了一类具有p-Laplacian算子和积分边界条件的分数阶微分方程解的存在性.当限定f(t,u(t))在两个不同区间上的范围以及满足"变异"的Lipschitz条件时,利用退化方程构造的Green函数及其性质,结合Guo-Krasnosel’skii不动点定理以及Banach压缩映射原理,分别证明了所研究问题的解的存在唯一性.In this paper,we study the existence of solutions for a class of fractional differential equations with p-Laplacian operator and integral boundary conditions.When the range of on two different intervals is limited and the Lipschitz condition of"variation"is satisfied,the existence and uniqueness of the solution of the problem are proved by using the Green function and properties constructed by the degenerate equation,Guo-Krasnosel’skii fixed point theorem and Banach contraction mapping principle.

关 键 词：P-LAPLACIAN算子 GREEN函数 不动点定理 BANACH压缩映射原理 正解 

分 类 号：O175[理学—数学]