Ground state of solutions for a class of fractional Schrödinger equations with critical Sobolev exponent and steep potential well

Abstract

In this paper, we study the following fractional Schrödinger equations: urn:x-wiley:mma:media:mma4527:mma4527-math-0001 where (−△)α is the fractional Laplacian operator with , 0≤s≤2α, λ>0, κ and β are real parameter. is the critical Sobolev exponent. We prove a fractional Sobolev‐Hardy inequality and use it together with concentration compact theory to get a ground state solution. Moreover, concentration behaviors of nontrivial solutions are obtained when the coefficient of the potential function tends to infinity.