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 $Lu=g\left(x,t,u\right)$ in $\Omega \times ℝ$ (where $\Omega \subset {ℝ}^N$ is a smooth bounded domain) for a wide class of Carathéodory functions $g:\Omega \times ℝ\times [0,\infty )\to ℝ$ satisfying some integrability and positivity conditions.