On positive solutions for some semilinear periodic parabolic eigenvalue problems ✩

For a bounded domain Ω in RN, N 2, satisfying a weak regularity condition, we study existence of positive and T -periodic weak solutions for the periodic parabolic problem Luλ = λg(x, t,uλ) in Ω × R, uλ = 0 on ∂Ω × R. We characterize the set of positive eigenvalues with positive eigenfunctions associated, under the assumptions that g is a Caratheodory function such that ξ → g(x, t, ξ)/ξ is nonincreasing in (0,∞) a.e. (x, t ) ∈ Ω × R satisfying some integrability conditions in (x, t ) and T 0 esssup x∈Ω inf ξ>0 g(x, t, ξ) ξ dt >0.  2002 Elsevier Science (USA). All rights reserved.