一类半线性椭圆型方程的边值问题

BOUNDARY VALUE PROBLEM OF A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS

讨论了如下的半线性椭圆型偏微分方程的边值问题Δｕ＋ｆ（｜ｘ｜，ｕ）＝０，ｘ∈Ω，ｕ（ｘ）＝０，ｘ∈Ω的径向解．其中ｎ≥２，Ω是Ｒｎ空间的单位开球．用Ｓｃｈａｕｄｅｒ不动点定理，在新的奇异性条件下。

In this paper, the following boundary value problem of a class of semilinear elliptic equations, is investigated, Δu+f(|x|,u)=0,x∈Ω, u(x)=0,x∈Ω, where n ≥2, Ω is the open unit ball of R n . The existence of radially symmetric solutions of (1) (2) under a new singular condition is established by using Schauder's fixed point theorem.