Uniqueness of Positive Radial Solutions of Δu + f(u) = 0 in ℝ n , II

We prove a uniqueness result for the positive solution of Δu + f(u) = 0 in R n which goes to 0 at ∞. The result applies to a wide class of nonlinear functions f, including the important model case f(u) = − u + u p , 1 < p < (n + 2)/(n − 2). The result is proved by reducing to an initial-boundary problem for the ODE u″ + (n − 1)/r + f(u) = 0 and using a shooting method