@Article{Cai2026,
author = "Cai, Li and Pu, Rong",
title = "Solutions with prescribed mass for the Sobolev-critical Kirchhoff equation with trapping potential",
journal = "Opuscula Math.",
year = "2026",
volume = "46",
number = "5",
pages = "641--678",
doi = "https://doi.org/10.7494/OpMath.202610121",
url = "https://doi.org/10.7494/OpMath.202610121",
abstract = "We study prescribed-mass solutions of a nonautonomous Kirchhoff equation with a purely Sobolev-critical nonlinearity and a nonnegative trapping potential. The trapping potential breaks the scaling invariance of the autonomous problem, while the critical nonlinearity causes loss of compactness. We establish a global compactness alternative for constrained Palais-Smale sequences and combine it with sharp energy estimates adapted to the nonlocal Kirchhoff term. Under suitable structural assumptions and an explicit energy-separation condition, we obtain a positive normalized ground state as a local minimizer of the constrained energy. For sufficiently small Kirchhoff parameter \(b\gt 0\), we further prove the existence of a distinct positive normalized solution at a mountain-pass level.",
keywords = "Kirchhoff equation, Sobolev-critical exponent, normalized ground state, mountain-pass solution",
issn = "1232-9274"
}