环形区域上含梯度项的椭圆边值问题的径向解  

Radial solutions for elliptic boundary value problems with gradient terms in annular domains

作　　者：李其祥 李永祥 LI Qixiang;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,甘肃兰州730070

出　　处：《浙江大学学报（理学版）》2023年第3期287-291,共5页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(12061062,11661071).

摘　　要：讨论了环形区域Ω={x∈R^(N)|r_(1)<|x|<r_(2)}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≥3,f:[r_(1),r_(2)]×R×R^(+)→R连续。在不假定非线性项f非负的情形下,当f(r,u,η)关于η满足Nagumo型条件时,运用上下解方法和截断函数技巧,获得了径向解的存在性。进一步,证明了在一定条件下径向解的唯一性。The existence and uniqueness of radial solutions are discussed for elliptic boundary value problems{-Δu=f(|x|,u,|∇u|),x∈Ω,u|∂Ω=0 whereΩ={x∈R^(N)|r_(1)<|x|<r_(2)},N≥3,f:[r_(1),r_(2)]×R×R^(+)→R is continuous.In the general case where the nonlinear term f is not assumed to be non-negative,when f(r,u,η)satisfies Nagumo-type condition onη,the existence of radial solutions is proved for the problem by using the method of lower and upper solutions and a truncating functional technique.Further,the uniqueness of radial solution is demonstrated under certain conditions.

关 键 词：椭圆边值问题 径向解 环形区域 上下解 

分 类 号：O175.15[理学—数学]