Abstract
We prove the existence of a solution, decaying to zero at infinity, for the second order differential equation
1/A(t) (A(t)u'(t))' + phi(t) + f(t, u(t)) = 0, t is an element of (a, infinity).
Then we give a simple proof, under some sufficient conditions which unify and generalize most of those given in the bibliography, for the existence of a positive solution for the semilinear second order elliptic equation
Delta u + phi(x, u) + g(|x|)x center dot del u = 0,
in an exterior domain of the Euclidean space R-n, n >= 3.