On the existence of positive solutions for periodic parabolic sublinear problems

Abstract

We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problems Lu=g(x,t,u) in Ω×ℝ (where Ω⊂ℝN is a smooth bounded domain) for a wide class of Carathéodory functions g:Ω×ℝ×[0,∞)→ℝ satisfying some integrability and positivity conditions.