Existence of solutions for asymptotically periodic fractional Schrödinger equation with critical growth

Abstract

In this paper, we investigate a class of asymptotically periodic fractional Schrödinger equation with critical growth (−Δ) u + V(x)u = (x, u) + |u| 2 * −2 u, x ∈ R N , where ∈ (0, 1), N > 2 , 2 * = 2N N−2 , (−Δ) denotes the fractional Laplacian of order. V and f are asymptotically periodic functions. Based on the principle of concentration compactness and variational methods, we obtain some new existence results for the above equation, which improve the related conclusions on this topic.