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

Abstract. We prove that nonnegative solutions of quasilinear elliptic prob-lems of the type (0.1) −∆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 RN, N ≥ 2, symmetric with respect to a hyperplane, f is a locally Lipschitz continuous function in [0,+∞) with f(0) < 0, and u is a weak solution in C1(Ω). The proof of this result uses the moving plane method as in [2] and can be adapted to more general geometric situations