含p-Laplacian算子的分数阶微分方程耦合系统边值问题解的存在性  

Existenceof Solutions to Boundary Value Problemsfor Coupled Systemsof Fractional Differential Equations with p -Laplacian Operators

作　　者：徐紫钰 吴克晴[1] XU Ziyu;WU Keqing(School of Science,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]江西理工大学理学院,江西赣州341000

出　　处：《长春师范大学学报》2024年第12期13-24,42,共13页Journal of Changchun Normal University

基　　金：国家自然科学基金项目“向量变分不等式投影型方法研究”(61364015)。

摘　　要：研究了在混合型边界条件下的分数阶微分方程边值系统,讨论在该条件下系统解的存在性.系统的非线性项与未知函数的分数阶导数密切相关.该系统含p-Laplacian算子,同时非线性项含两个分数阶导数.首先将该系统转化成非线性项不含分数阶导数的耦合系统,然后基于不动点定理获得该系统解的存在性定理,并结合一个实例说明主要结果的实用性.We investigated the boundary value system of fractional differential equations under mixed boundary conditions,and at the same time,we discussed the existence of its solutions under these conditions.The nonlinear terms of the system are closely related to the fractional derivatives of unknown functions.This system contains p-Laplacian operator,with its nonlinear terms containing two derivatives.Firstly,the system is transformed into a nonlinear coupled system without fractional derivatives.Then,through some fixed point theorems,the existence theorem of the solution is obtained respectively.Finally,we combined a concrete example to highlight the practicability of the main results.

关 键 词：边值系统 不动点定理 解的存在性 P-LAPLACIAN 

分 类 号：O175.8[理学—数学]