摘要
针对一类非线性项含未知分数阶导函数,且带p-Laplacian算子的Hilfer分数阶微分方程边值问题,利用微分方程及边值条件计算出对应线性微分方程的解及Green函数并验证其性质;在自定义的锥上构造一个全连续算子,将解与算子不动点产生联系,再通过2个经典不动点定理的运用,分别得到问题至少有2个和3个正解充分性条件。研究进一步推广前人研究成果。
For a class of Hilfer fractional differential equation boundary value problems with nonlinear terms containing unknown fractional derivative functions and involving the p-Laplacian operator,the solutions of the corresponding linear differential equations and the Green function is calculated using the differential equations and boundary value conditions,and its properties are verified.A completely continuous operator is constructed on a self-defined cone,and the solutions are related to the fixed points of the operator.By applying 2 classical fixed point theorems,sufficient conditions for the existence of at least 2 and 3 positive ions are obtained respectively.The research further extends the previous results.
作者
钱英洁
叶欢
孟凡猛
周先锋
QIAN Yingjie;YE Huan;MENG Fanmeng;ZHOU Xianfeng(School of Mathematical Sciences,Anhui University,230601,Hefei,Anhui,China)
出处
《淮北师范大学学报(自然科学版)》
2025年第4期1-6,共6页
Journal of Huaibei Normal University(Natural Sciences)
基金
国家自然科学基金项目(11471015)。
