各向异性Laplace算子的一个非线性Picone恒等式及其应用  

A NONLINEAR PICONE IDENTITY FOR ANISOTROPIC LAPLACE OPERATOR AND ITS APPLICATIONS

作　　者：冯廷福 张克磊[2] FENG Ting-fu;ZHANG Ke-lei(School of Mathematics,Kunming University,Kunming 650214,China;School of Mathematics and Computating Sciences,Guilin University of Electronic Science and Technology,Guilin 541004,China)

机构地区：[1]昆明学院数学学院,云南昆明650214 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《数学杂志》2020年第3期283-290,共8页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11701453,11701322);Guangxi Natural Science Foundation(2017GXNSFBA198130);Scientific Research Fund of Yunnan Provincial Education Department(2019J0556)。

摘　　要：本文针对各向异性Laplace算子,建立了一个非线性Picone恒等式.作为它的应用,得到了各向异性椭圆方程的Sturmian比较原理、各向异性椭圆系统的Liouville定理和广义的各向异性Hardy型不等式.A nonlinear Picone identity for anisotropic Laplace operator is established in this paper.As applications,a Sturmian comparison principle to an anisotropic elliptic equation,a Liouville’s theorem to an anisotropic elliptic system and a generalized anisotropic Hardy type inequality are obtained.

关 键 词：各向异性Laplace算子 非线性Picone恒等式 应用 

分 类 号：O175.29[理学—数学]