Uniqueness of radially symmetric positive solutions for [formula omitted] in an annulus

Abstract

In this article we prove that the semi-linear elliptic partial differential equation − Δ u + u = u p in Ω , u > 0 in Ω , u = 0 on ∂ Ω possesses a unique positive radially symmetric solution. Here p > 1 and Ω is the annulus { x ∈ R N | a < | x | < b } , with N ⩾ 2 , 0 < a < b ⩽ ∞ . We also show the positive solution is non-degenerate.