A numerical algorithm for finding positive solutions for classes of p-Laplacian equations

In this paper we investigate numerically positive solution of the equation −Δpu = g(λ, u) with Dirichlet boundary condition in a boundary domain Ω in RN; N ⩾ 2 with ∂Ω of class C2 and connected for λ > 0 and p > 1. In particular, we establish existence results for classes of nondecreasing, p-sublinear functions g(λ, u) belonging to C1([0, ∞)). We will show that in which range of λ, this problem achieves a numerical solution.