On the antimaximum principle for the p -Laplacian and its sublinear perturbations

We investigate qualitative properties of weak solutions of the Dirichlet problem for the equation -Δ _p u = λ m(x)|u|^p-2u+ η a(x)|u|^q-2u+ f(x) in a bounded domain Ω⊂ℝ^N , where q

1 solutions of the unperturbed problem satisfy the antimaximum principle in a right neighborhood of the first eigenvalue of the p -Laplacian provided m,f ∈ L^γ (Ω ) with γ >N . For completeness, we also investigate the existence of solutions.