Abstract

Using a new gradient estimate, we prove several theorems on the existence of radial ground states For the n-Laplace equation div(-del u-(n-2) del u) + f(u) = 0 in R-n,n > 1, and the existence of positive radial solutions for the associated Dirichlet-Neumann free boundary value problem in a ball. We treat exponentially subcritical. critical, and supercritical nonlinearities f(u), which also are allowed to have singularities at zero. Moreover, we show that the local behavior off at zero affects the existence in a crucial way: this allows us to prove the existence of ground states for a large class of functions f(ll) without imposing any restriction on their growth for large. (C) 2000 Academic Press.