球外部区域上非线性椭圆型方程的正径向解

Positive Radial Solutions of Nonlinear Elliptic Equations in Exterior Domains of Ball

中文关键词:  椭圆边值问题  球外部区域  正径向解  闭凸锥

英文关键词:elliptic boundary value problem  exterior domain of ball  positive radial solution  closed convex cone

中文摘要:

      本文讨论球外部区域Ω={x∈R^N||x|>R}上非线性椭圆边值问题-Δ u=g(|x|)f(u),αu+β(?u)/(?n)|_?Ω=0,u(∞)=0 正径向解的存在性,其中g(r),f(u)为非负连续函数.在g(r)满足条件0<∫_R^∞rg(r)dr<∞,f(u)关于u超线性或次线性增长的情形,获得了该问题正径向解的存在性.

英文摘要:

      This paper discusses the existence of positive radial solutions for nonlinear elliptic boundary value problem in exterior domain Ω= {x ∈ R^N|||x||> R}:-Δ u=g(|x|)f(u),αu+β(?u)/(?n)|_?Ω=0,u(∞)=0 where g(r) and f(u) are nonnegative continuous functions. The existence of positive radial solution is obtained under the conditions that 0 <∫_R^∞rg(r)dr≤∞ and f(u) is either superlinear or sublinear.