A numerical method for finding positive solutions of a superlinear Dirichlet problem

In this work we present a numerical approach for finding positive solutions of the type −Δu = λf(u) for x ∈ Ω, with Dirichlet boundary condition, where f is a superlinear function of u. We will show in which range of λ, this problem achieves multiple numerical solutions and what is the behavior of the branches of solutions.