Uniqueness of positive solutions of nonlinear elliptic equations with exponential growth

By combining a technique inspired to the theory of sublinear elliptic equations with the Emden-Fowler inversion technique of Atkinson and Peletier, we obtain uniqueness of positive solutions of the following equation -Δu = λueu θ in B, u > 0, u = 0 on ∂B, where B ⊂ ℝn is the ball of radius one, λ > 0 and 1 < ν ≤ 2.