球外部区域上含梯度项椭圆边值问题的径向解

Existence of Radial Solutions for Elliptic Boundary Value Problem with Gradient Terms in Exterior Domains

用Leray-Schauder不动点定理,考虑球外部区域Ω={x∈RN:■上含梯度项的椭圆边值问题:■径向解的存在性与唯一性,其中:N≥3;R0>0;K:[R0,∞)→R+和f:[R0,∞)×R×R+→R连续.当系数函数K(r)=O(1/r2(N-1))(r→+∞)时,在允许非线性项f(r,u,η)关于u,η超线性增长的情形下,给出该问题径向解的存在性与唯一性证明.

Using the Leray-Schauder fixed point theorem, we consider the existence and uniqueness of radial solutions for elliptic boundary value problems with gradient term■where Ω={x∈RN: ■: [R0,∞)→R+ and f: [R0,∞)×R×R+→R are continuous. When the coefficient function K(r)=O(1/r2(N-1))(r→+∞), under the condition that the nonlinear term f(r,u,η) allows superlinear growth on u and η, we prove the existence and uniqueness of radial solutions of the problem.