Uniqueness of radially symmetric positive solutions for −Δu+u=up−Δu+u=up in an annulus

In this article we prove that the semi-linear elliptic partial differential equation−Δu+u=upin Ω,u>0in Ω,u=0on ∂Ω possesses a unique positive radially symmetric solution. Here p>1p>1 and Ω   is the annulus {x∈RN|a<|x|