UNIQUENESS OF POSITIVE SOLUTIONS OF DELTA-U-N, N-GREATER-THAN-OR-EQUAL-TO-3(F(U)=0 IN R)

We study the uniqueness of radial ground states for the semilinear ell iptic partial differential equation Delta u + f(u) = 0 () in R-N. We assume that the function f has two zeros, the origin and u(0) > 0. Abo ve u(0) the function f is positive, is locally Lipschitz continuous an d satisfies convexity and growth conditions of a superlinear nature. B elow u(0), f is assumed to be nonpositive, non-identically zero and me rely continuous. Our results are obtained through a careful analysis o f the solutions of an associated initial-value problem, and the use of a monotone separation theorem. It is known that, for a large class of functions f, the ground states of () are radially symmetric. In thes e cases our result implies that () possesses at most one ground state .