Existence of Positive Solutions of Schrodinger Equations with Vanishing Potentials

We prove the existence of at least one positive solution for a Schrodinger equation in RNof type with a vanishing potential at infinity and subcritical nonlinearity f. Our hypotheses allow us to consider examples of nonlinearities which do not verify the Ambrosetti-Rabinowitz condition, neither monotonicity conditions for the function f(x,s)/s. Our argument requires new estimates in order to prove the boundedness of a Cerami sequence. © 2020 American Institute of Mathematical Sciences. All rights reserved.