Indefinite Perturbations of the Eigenvalue Problem for the Nonautonomous p-Laplacian

We consider an indefinite perturbation of the eigenvalue problem for the nonautonomous p-Laplacian. The main result establishes an exhaustive analysis in the nontrivial case that corresponds to noncoercive perturbations of the reaction. Using variational tools and truncation and comparison techniques, we prove an
existence and multiplicity theorem which is global in the parameter. The main result of this paper establishes the existence of at least two positive solutions in the case of small perturbations, while no solution exists for high perturbations of the quasilinear term in the reaction.