MULTIPLICITY OF POSITIVE SOLUTIONS TO SCHRÖDINGER-TYPE p-LAPLACIAN PROBLEMS

MULTIPLICITY OF POSITIVE SOLUTIONS TO SCHRÖDINGER-TYPE p-LAPLACIAN PROBLEMS

We establish a multiplicity result for positive solutions to a Schrödinger-type p-Laplacian problem: -∆_pu + V (x)|u|^p-2u = λf(u) in Ω, u = 0 on ∂Ω, where ∆_pu = div(|∇_u|^p-2|∇_u) is the p-Laplacian operator, p ≥ 1, Ω is a bounded domain in ℝ^N, N ≥ 2, λ is a positive parameter, V ∈ L^∞(Ω) and f : [0,∞) → (0,∞) is a continuous function. In particular, when f is p- sublinear at infinity, we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub and supersolution method.