We study the equation r 2 d 2 f / d r 2 + f = f 3 with the boundary conditions f ( 1 ) = 0 , f ( ∞ ) = 1 , and 0$"> f ( r ) > 0 for 1 < r < ∞ . The existence of the solution is proved using a topological shooting argument. And the uniqueness is proved by a variation method.