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In this paper, we study the following fractional Schrödinger equation involving critical or supercritical exponentwhere 0&lt; s &lt;1,  N &gt;2 s ,,,,denotes the fractional Laplacian of order  s  and  f  is a continuous superlinear but subcritical nonlinearity. When  V  and  f  are asymptotically periodic in  x , we prove that the equation has a ground state solution for smallby the Nehari method. Our main contribution is that we are able to deal with the supercritical case.

Ground states for fractional Schrödinger equations involving critical or supercritical exponent