Positive solutions to a Dirichlet problem with non-Lipschitz nonlinearities

Abstract

Let Ω be a bounded smooth domain in ℝN. We study the existence of positive solutions to the Dirichlet problem -Δu = (1 - u)us-1 - λur-1, in Ω, u = 0, on ∂Ω, where 1 < r < s ≤ 2, and λ > 0. In particular, we answer to some questions posed in the recent paper [3] where this problem was considered.