Uniqueness of solutions of nonlinear Dirichlet problems

In this paper, we consider the uniqueness of radial solutions of the nonlinear Dirichlet problem Δu + f{hook}(u) = 0 in Ω with u = 0 on ∂Ω, where Δ = ∑_{i = 1}ⁿ ∂² ∂x_i²,f{hook} satisfies some appropriate conditions and Ω is a bounded smooth domain in Rⁿ which possesses radial symmetry. Our uniqueness results apply to, for instance, f{hook}(u) = u^p, p > 1, or more generally λu + ∑_{i = 1}^k a_iu^pi, λ ≥ 0, a_i > 0 and p_i > 1 with appropriate upper bounds, and Ω a ball or an annulus.