Abstract :
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.
