It is shown that for a Dirichlet's periodic problema studied by Lazer: L(u) = g(x,t,u)+f 1 (x,t)+s𝜙(x,t) in Ω xR u(x,t+T) ≡ u(x,t), u|∂ Ω xR= 0 where Ω is a bounded domain in R N ,and certain restrictions are assumed for g, f 1 , and 𝜙, there exists a number ∝(f 1 ) such that the problem has at least two solution if s < ∝(f 1 ), and at least one if s = ∝(f 1 ).
