Two numerical algorithms for finding solutions of multiparameter semipositone Dirichlet problems

In this paper, we investigate numerically positive solutions of the equation −Δu = λf(x, u) + μg(x, u) with Dirichlet boundary condition in a bounded domain Ω for λ > 0, μ ∈ R using sub-super solution algorithm and mountain pass algorithm. We will show that in which range of λ, this problem achieves numerical solutions.