Local uniqueness of constraint minimizers for double nonlocal functional

Abstract

This paper is concerned with constraint minimizers of the fractional Kirchhoff type equations in R2. On the basis of the asymptotic behaviors, we further show the local uniqueness of constraint minimizers by setting Pohozăev identity for the double nonlocal equation. As a continuation of [32], our result complements the research of asymptotic behaviors about such equations. Moreover, we believe that the nonlocal Pohozăev identity established in this paper can be widely used in the study of other equations.