A Landesman–Lazer type result for periodic parabolic problems on RNRN at resonance

We are concerned with TT-periodic solutions of nonautonomous parabolic problem of the form ut=Δu+V(x)u+f(t,x,u)ut=Δu+V(x)u+f(t,x,u), t>0t>0, x∈RNx∈RN, with V∈L∞(RN)+Lp(RN)V∈L∞(RN)+Lp(RN), where 2