一类具有p-Laplacian算子的高阶非线性分数阶微分方程的正解  

Positive Solutions of a Class of Higher Order Nonlinear Fractional Differential Equations with p-Laplacian Operator

作　　者：许佰雁[1] 姜亦成[2] 杨洋[1] XU Bai-yan;JIANG Yi-cheng;YANG Yang(Basic Research Section,Changchun Guanghua University,Changchun 130033,China;College of Science,Qiqihar University,Qiqihar 161006,China)

机构地区：[1]长春光华学院基础教研部,吉林长春130033 [2]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006

出　　处：《数学的实践与认识》2021年第9期283-291,共9页Mathematics in Practice and Theory

基　　金：吉林省教育厅“十三五”科学技术项目(JJKH20171027KJ);吉林省发改委基金(2019C054-7);齐齐哈尔大学博士科研启动基金(340242);长春光华学院青年科研重点基金项目(QNJJZD2019005)。

摘　　要：通过构造Green函数的性质及锥上的不动点定理,研究一类带有p-Laplacian算子且边界条件为分数阶导数的高阶非线性分数阶微分方程的正解问题;并通过构造超线性和次线性条件,证明了边界问题正解的存在性.By constructing the properties of Green’s function and the fixed point theorem on the cone,this paper studies the positive solutions of a class of higher-order nonlinear fractional differential equations with p-Laplacian operator and fractional derivative boundary conditions,and proves the existence of positive solutions of boundary value problems by construction superlinear and sublinear conditions.

关 键 词：分数阶微分方程 边值问题 GREEN函数 不动点定理 正解 

分 类 号：O175[理学—数学]