Existence theorems for degenerate Schrödinger equations involving a singular potential and an indefinite sign perturbation

Abstract

We study a degenerate quasilinear problem involving a singular potential and some bounded weights. The equation is perturbed by a critical nonlinear term and an indefinite sign perturbation involving a real parameter. Under suitable assumptions on the potentials and on the real parameter we use two different critical point techniques, in order to reveal two types of solutions. The proofs rely on variational arguments based on the Mountain-Pass Theorem, Ekeland's Variational Principle and energy estimates.