Uniqueness for a Semilinear Elliptic Equation in Non-contractive Domains Under Supercritical Growth Conditions

Abstract

We apply the Pohozaev identity to sub-domains of a tubular neighbourhood of a closed or broken curve in ℝn and establish uniqueness results for the smooth solutions of the Dirichlet problem for -Δu + |u|p-1 u = 0. We require the domain to be in ℝn with n ≥ 4 and with p > (n + 1)/(n - 3).