Concentration and Local Uniqueness of Constrained Minimizers for the Kirchhoff Equation With a Trapping Potential

This paper investigates the ‐normalized minimizers of a Kirchhoff‐type energy functional. We first establish the concentration behavior of minimizers for the case with . Since the explicit form of minimizers is unavailable when the potential vanishes, we derive crucial asymptotic properties to overcome this difficulty. Furthermore, we prove the local uniqueness of minimizers for sufficiently small . In contrast to existing results, our approach introduces novel identities that streamline the classical analysis.