A numerical method to find positive solution of semilinear elliptic Dirichlet problems

In this work we present a numerical approach for finding positive solutions for the elliptic problems of the type −Δu = λf(x)g(u) for x ∈ Ω, with Dirichlet boundary condition. 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 solutions.