One-dimensional singular problems involving the p-Laplacian and nonlinearities indefinite in sign

Abstract

Let Ω be a bounded open interval, let p > 1 and γ >, and let m : Ω → ℝ be a function that may change sign in Ω. In this article we study the existence and nonexistence of positive solutions for one-dimensional singular problems of the form - (|u′|p-2u′)′ = m(x) u-γ in Ω, u = 0 on ∂Ω. As a consequence we also derive existence results for other related nonlinearities.