On positive solutions of a class of nonlinear elliptic equations

We investigate the existence of positive solutions vanishing as |x|→+∞|x|→+∞ to the semilinear elliptic equation Δu+f(x,u)+g(|x|)x⋅∇u=0, |x|>A>0|x|>A>0, in RnRn, n≥3n≥3, under mild assumptions on the functions ff, gg. Conditions for these solutions to be radial are also given.