外部区域上p-Laplace方程的径向对称解  

Radial Symmetric Solutions of p-Laplace Equations on Exterior Domains

作　　者：李鹏博 李永祥 LI Pengbo;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou Gansu 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《广西师范大学学报（自然科学版）》2023年第5期69-75,共7页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(12061062,11661071)。

摘　　要：本文讨论R^(N)(N≥2)中外部区域Ω={x∈RN:|x|>r_(0)}上一类p-Laplace边值问题径向对称解的存在性。不同于已有文献,对连续函数f:R→R,不要求f非负,在其满足适当不等式条件下,应用Leray-Schauder不动点定理获得径向对称解的存在性,并在此基础上进一步讨论径向对称解的唯一性。The existence of radial symmetric solutions of a class of p-Laplace equation on the exterior domainΩ={x∈R^(N):x>r_(0)}(N≥2)is investigated in this paper.For continuous function f:R→R,unlike the previous literatures,the condition that f is nonegative is removed.Under the condition that f satisfies an appropriate inequality,an existence result of radial symmetric solutions is obtained by applying the Leray-Schauder fixed point theorem.On this basis,the uniqueness of radial symmetric solutions is discussed.

关 键 词：外部区域 P-LAPLACE方程 径向对称解 LERAY-SCHAUDER不动点定理 

分 类 号：O175.8[理学—数学]