Non-degeneracy of bubbling solutions for fractional Schrödinger equation and its application

Abstract

We consider the following fractional Schrödinger equation:(−Δ)su+V(y)u=u2s⁎−1, in RN, where 12≤s<1, 2s⁎=2NN−2s is the critical Sobolev exponent, and V(y) is a positive function. By using four types of local Pohozaev identities, we prove a non-degeneracy result of the positive bubbling solutions. We also give an application of the non-degeneracy result.