Ground States of Nonlocal Fractional Schrödinger Equations with Potentials Well

Abstract

Inspired by Alves and Souto [2], we investigate the existence of nontrivial solutions to a class of fractional Schrödinger equations with potentials well. Taking the superlinear nonlinearities into consideration, we obtain the existence of nontrivial solutions by loosing monotonicity. Furthermore, a ground state solution is established. This was proved in [7] that (1.1) can be reduced to the classical Schrödinger equation, since (− ) s can be changed to the standard Laplace − as s → 1.