An elementary proof of the boundedness of eigenfunctions for the negative p-laplacian operator under dirichlet boundary conditions

Nonlinear eigenvalue problems are actively studied subject in recent research. In this paper, we are concerned with the boundedness of eigenfunctions for the following eigenvalue problems: (Formula) where Δ_p is the p-Laplacian operator and ξ ∈ L^∞(Ω), ξ ≥ 0. Though the boundedness of eigenfunctions for the above boundary value problems is well-known, most of the proofs are a little complicated because they are based on the boundedness theorem which is applicable to more general equations. Therefore, we give a proof that involves only elementary techniques.