Existence of solutions for asymptotically periodic fractional Schrödinger equation.

In this paper we study the following nonlinear fractional Schrödinger equation ( − Δ ) s u + V ( x ) u = f ( x , u ) , x ∈ R N , where s ∈ ( 0 , 1 ) , ( − Δ ) s is the fractional Laplacian operator of order s , and V , f are asymptotically periodic functions in x . Under suitable conditions, the existence of nontrivial solution is obtained by using variational methods and concentration compactness argument. [ABSTRACT FROM AUTHOR]