双曲空间上p(x)-Laplace算子的Picone恒等式及其应用  

A Picone's identity for the p(x)-Laplace operator on hyperbolic space

作　　者：刘娜 余路娟 LIU Na;YU Lujuan(College of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《周口师范学院学报》2024年第2期5-11,共7页Journal of Zhoukou Normal University

摘　　要：Picone恒等式在偏微分方程的研究中起着重要的作用,其应用非常广泛。把欧式空间?~N中的p(x)-Laplace算子推广到双曲球模型Β~N和双曲半模型Η~N上,建立双曲空间上p(x)-Laplace算子相对应的Picone恒等式并给出这些恒等式的应用,从而把欧氏空间中变指数问题的相关结果推广到双曲空间上。Picone’s identity plays a crucial role in the study of partial differential equations,and its applications are very extensive.In this paper,we extend the p(x)-Laplace operator from Euclidean space to hyperbolic space,including both the ball modelΒNand the half space modelΗN.We establish Picone's identities corresponding to the p(x)-Laplace opera-tor on hyperbolic space and provide applications for these identities.Therefore,the relevant results of the variable exponents problem in Euclidean space can be generalized to hyperbolic space.

关 键 词：PICONE恒等式 p(x)-Laplace算子 双曲空间 

分 类 号：O175.2[理学—数学]