On some singular periodic parabolic problems

Let Ω⊂RN be a smooth bounded domain. We study existence of positive solutions for some singular Dirichlet periodic parabolic problems of the form Lu=-g(x,t,u)+λh(x,t,u) in Ω×R, where s→g(x,t,s) is nonincreasing and has a singularity at s=0 that behaves like s-α and s→h(x,t,s) is nondecreasing, superlinear at the origin and sublinear at infinity. These results remain true for the corresponding elliptic problems.