Uniqueness of solutions of nonlinear Dirichlet problems

AbstractIn this paper, we consider the uniqueness of radial solutions of the nonlinear Dirichlet problem Δu + ƒ(u) = 0 in Ω with u = 0 on ∂Ω, where Δ = ∑i = 1n∂2∂xi2,ƒ satisfies some appropriate conditions and Ω is a bounded smooth domain in Rn which possesses radial symmetry. Our uniqueness results apply to, for instance, ƒ(u) = up, p > 1, or more generally λu + ∑i = 1k aiupi, λ ⩾ 0, ai > 0 and pi > 1 with appropriate upper bounds, and Ω a ball or an annulus