The Ambrosetti–Prodi Problem for thep-Laplace Operator

In this work we study the existence of a solution for the problem − Δ p u = f(u) + tΦ(x) + h(x), with homogeneous Dirichlet boundary conditions. Here the nonlinear term f(u) is a so-called jumping nonlinearity. In the proofs we use topological arguments and the sub-supersolutions method, together with comparison principles for the p-Laplacian.