Abstract: Working on the p-Laplacian operator, we explore the well known Ambrosetti-Prodi problem, extending previous achievements for the Laplacian obtained in the paper of De Figueiredo and Jianfu, 1999. We prove that a negative solution for the problem is obtained as a global minimum of a related p-linear problem and a second solution is found by variational methods. We reach the same restriction to dimension N, found on the mentioned paper when p = 2.