单位球上含梯度项的椭圆边值问题径向解的存在性与唯一性  

Existence and Uniqueness of Radial Solutions to EllipticBoundary Value Problem with Gradient Terms on the Unit Ball

作　　者：唐颖 李永祥 TANG Ying;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2021年第5期1009-1014,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061062,11661071).

摘　　要：用Schauder不动点定理,讨论单位球Ω={x∈ℝN:x<1}上含梯度项的椭圆边值问题:-Δu=f(x,u,u),x∈Ω,u∂Ω=0径向解的存在性与唯一性,其中N≥2,f:[0,1]×ℝ×ℝ+→ℝ连续.在允许非线性项f(r,ξ,η)关于ξ,η超线性增长的情形下,获得了该问题径向解及正径向解的存在性结果.此外,还讨论该问题径向解的唯一性.By using Schauder fixed-point theorem,we discuss the existence and uniqueness of radial solutions to elliptic boundary value problem with gradient terms-Δu=f(x,u,u),x∈Ω,u∂Ω=0,whereΩ={x∈ℝN:x<1},N≥2,f:[0,1]×ℝ×ℝ+→ℝis continuous.The existence results of radial solutions and positive radial solutions to the problem are obtained under the condition that the nonlinear term f(r,ξ,η)is allowed to grow superlinearly with respect toξandη.In addition,we also discuss the uniqueness of radial solutions of this problem.

关 键 词：椭圆边值问题 单位球 径向解 SCHAUDER不动点定理 

分 类 号：O175.25[理学—数学] O177.91[理学—基础数学]