On positive solutions of a class of nonlinear elliptic equations

We investigate the existence of positive solutions vanishing as x ->+infinity to the semilinear elliptic equation Delta u + f (x, u) + g(x)x . del u = 0, x > A > 0, in R-n, n >= 3, under mild assumptions on the functions f, g. Conditions for these solutions to be radial are also given