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| 一类具有P-Laplacian算子的非线性分数阶微分方程解的存在性研究 | |
| 引用本文： | 许佰雁,姜亦成,杨洋. 一类具有P-Laplacian算子的非线性分数阶微分方程解的存在性研究[J]. 数学的实践与认识, 2021, 0(6): 290-296 |
| 作者姓名： | 许佰雁 姜亦成 杨洋 |
| 作者单位： | 长春光华学院基础教研部;齐齐哈尔大学理学院 |
| 基金项目： | 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,利用Banach不动点定理,研究了一类带有P-Lapalcian算子Caputo型非线性分数阶微分方程的正解问题;并通过构造第二变元的Lipschitz条件,在P-Lapalcian算子参数取不同值的范围下,分别证明了边值问题正解的存在性与唯一性. |
| 关 键 词： | 分数阶微分方程 边值问题 Green函数 Banach不动点定理 P-Laplacian算子 正解 |
Existence of Solutions for a Class of Fractional Differential Equations with P-Laplacian Operators and Integral Boundary Conditions |
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| XU Bai-yan,JIANG Yi-cheng,YANG Yang. Existence of Solutions for a Class of Fractional Differential Equations with P-Laplacian Operators and Integral Boundary Conditions[J]. Mathematics in Practice and Theory, 2021, 0(6): 290-296 | |
| Authors: | XU Bai-yan JIANG Yi-cheng YANG Yang |
| Affiliation: | (Basic Research Section,Changchun Guanghua University,Changchun 130033,China;College of Science,Qiqihar University,Qiqihar 161006,China) |
| Abstract: | By constructing the properties of Green function and using the Banach fixed point theorem,we study the positive solution of a class of nonlinear fractional differential equation with p-Laplacian operator Caputo type.By constructing the Lipschitz condition of the second variable,we prove the existence and uniqueness of the positive solution of the boundary value problem in the range of different parameters of p-Laplacian operator. |
| Keywords: | fractional differential equations boundary value problem green function banach fixed point theorem p-Laplacian operator positive solution |
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