Uniqueness of radially symmetric positive solutions for -Delta u+u=u(p) in an annulus

Abstract

In this article we prove that the semi-linear elliptic partial differential equation -Delta u + u = u(p) in Omega

u > 0 in Omega. u = 0 on partial derivative Omega

possesses a unique positive radially symmetric solution. Here p > 1 and Omega is the annulus (x epsilon R-N vertical bar a < vertical bar x vertical bar < b), with N >= 2, 0 < a < b <= infinity. We also show the positive solution is non-degenerate.