Existence of strictly positive solutions for sublinear elliptic problems in bounded domains

Abstract

Let Ω be a smooth bounded domain in RN and let m be a possibly discontinuous and unbounded function that changes sign in Ω. Let f : [0,∞) → [0,∞) be a nondecreasing continuous function such that k1 ξp ≤ f (ξ) ≤ k2 ξp for all ξ ≥ 0 and some k1 ,k2 > 0 and p ∈ (0,1). We study existence and nonexistence of strictly positive solutions for nonlinear elliptic problems of the form −∆u = m (x) f (u) in Ω, u = 0 on ∂Ω.