A class of asymptotically periodic fractional Schrödinger equations with critical growth

In this paper, we study a class of fractional Schrödinger equations in [Formula: see text] of the form [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] is the critical Sobolev exponent, [Formula: see text] is a positive potential bounded away from zero, and the nonlinearity [Formula: see text] behaves like [Formula: see text] at infinity for some [Formula: see text], and does not satisfy the usual Ambrosetti–Rabinowitz condition. We also assume that the potential [Formula: see text] and the nonlinearity [Formula: see text] are asymptotically periodic at infinity. We prove the existence of at least one solution [Formula: see text] by combining a version of the mountain-pass theorem and a result due to Lions for critical growth.