Existence of global positive solutions of semilinear elliptic equations

Using a very simple approach, we prove the existence of asymptotically vanishing global positive solutions of the semilinear elliptic equation Δu+f(x,u)+g(|x|)x⋅∇u=0 in all of RnRn, n≥3n≥3. In particular, earlier conditions on the negative part of the function ff are dropped.