Existence results for an indefinite unbounded perturbation of a resonant Schrödinger equation

We study existence results for a nonlinear Schrödinger equation at resonance. The nonlinearity is assumed to change sign, be unbounded but sublinear with a power like growth at infinity. Under a suitable coercivity assumption on the primitive of the nonlinear term on the kernel of the Schrödinger operator, we prove the existence of at least one solution.