Abstract
In the present paper we deal with a nonlinear fractional Schrödinger equation in of the formwhere is a parameter, , , V(x) is a continuous potential, and is the Riesz potential. By applying variational methods and the Ljusternik–Schnirelmann category theory, under some suitable conditions on V(x) we prove the existence and multiplicity of solutions for the above equation when the parameter is sufficiently small. Moreover, the concentration behavior of solutions for the fractional Schrödinger equation is also explored.
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