Elliptic Problems with Nonlinearities Indefinite in Sign

LetΩ⊂RN,N⩾3, be a bounded open set with smooth boundary andλ∈R. We study the Dirichlet problem,[formula]with 1<q<pandh, k∈L∞(Ω) nonnegative functions. We prove existence, nonexistence and multiplicity results depending onλand according to the integrability properties of the ratiokp−1/hq−1.