On Positive Solutions of a Superlinear Dirichlet Problem with a Weight Function

We use variational method to study the existence of a positive solution of the equation −Δu(x) = λg(x)u(x)(1 + u(x)) with Dirichlet boundary condition to the case where g is positive. We present a numerical approach for finding positive solutions and we will show that in which range of λ, this problem achieves a numerical solution and what is the behavior of the branch of this solution.