非线性椭圆方程自由边值问题球对称解的存在性

给出了如下的非线性椭圆方程自由边值问题-Δu=λu+(1+ε)u+p,x∈B Rn,u|Ω=μ,∫Ωnu=-M(1)在C0,1]中的球对称解的存在性.并得到比上述问题更一般的非线性椭圆方程自由边值问题-Δu=h(u),x∈B Rn,u|Ω=μ,∫Ωun=-M,在C0,1]中的球对称解的存在性,其中B为Rn中的单位球,p>1,λ>0,μ<0,M>0,ε>0;λ,μ,M,ε均为常数,n为正整数.

Existence of Radial Solution to the Free Boundary Problems for Nonlinear Elliptic Equation

This paper gives the existence of radial solution in C to the following free boundary problem for nonlinear elliptic equation:-Δu=λu+(1+ε)up+,x∈BRn,u|Ω=μ,∫Ωun=-MFurthermore,it shows that the following free boundary problem for nonlinear elliptic equation,which is more general than the above problem,possesses radial solution in C:-Δu=h(u),x∈BRn,u|Ω=μ,∫Ωun=-M,Where B is the unit ball in Rn.p>1,λ>0,μ<0,M>0,ε>0;λ,μ,M,ε are some sonstants.n is a positive integer.