Boundary-value Problems for the One-dimensional p-Laplacian with Even Superlinearity

Abstract

This paper is concerned with a study of the quasilinear problem −(|uI|p−2uI)I = |u|p − λ, in (0, 1) , u(0) = u(1) = 0, where p >1 and λ ∈ R are parameters. For λ > 0, we determine a lower bound for the number of solutions and establish their nodal properties. For λ ≤ 0, we determine the exact number of solutions. In both cases we use a quadrature method.