Abstract

By construction sub and supersolutions for the following semilinear elliptic equation −△u(x)=λg(x)f(u(x)), x∈ℝn 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:ℝn→ℝ such that g is smooth and is negative at infinity.