A strong maximum principle for a class of non-positone singular elliptic problems

Abstract

We prove that nonnegative solutions of quasilinear elliptic problems of the type (0.1) {-Δ_pu=f(u) in Ω, 1 < p ≤ 2 u = 0 on ∂Ω are actually positive in Ω , under the following assumptions: Ω is a regular bounded strictly convex domain in ,R^N,N ≥ 2 symmetric with respect to a hyperplane, ƒ is a locally Lipschitz continuous function in [0,+ ∞) with ƒ(0) <0, and u is a weak solution in C¹(Ω̅). The proof of this result uses the moving plane method as in [2] and can be adapted to more general geometric situations.