Semiclassical states for fractional Schrödinger equations with critical nonlinearities

Abstract

In this paper, we consider the following fractional Schrödinger equation where is a parameter, is the fractional Laplacian and is a superlinear and subcritical nonlinearity. Under a local condition imposed on the potential function, combining the penalization method and the concentration‐compactness principle, we prove the existence of a positive solution for the above equation.