Uniqueness and non-degeneracy of solutions for nonlinear fractional Schrodinger equation with perturbation

This paper concerned a fractional Schr & ouml;dinger equation in whole space, for epsilon > 0 is a small parameter, epsilon(2s)(-Delta)(s)u + V(x)u = |u|(p-2)u, where 12<s<1, N > 1 and 2<p<2N/N-2s. We prove the non-degeneracy and uniqueness of bubble solutions by using local Pohozaev identity and finite dimensional reduction, which are the cornerstones to construct different type solutions.