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

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.