By construction sub and supersolutions for the following semilinear elliptic equation − △ u ( x ) = λ g ( x ) f ( u ( x ) ) , x ∈ ℝ n which arises in population genetics, we derive some results about the theory of existence of solutions as well as asymptotic properties of the solutions for every n and for the function g : ℝ n → ℝ such that g is smooth and is negative at infinity.