TY  - JOUR
ID  - Cai2026
LB  - Cai2026
AU  - Cai, Li
AU  - Pu, Rong
TI  - Solutions with prescribed mass for the Sobolev-critical Kirchhoff equation with trapping potential
ST  - Solutions with prescribed mass for the Sobolev-critical Kirchhoff equation with trapping potential
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 5
SP  - 641
EP  - 678
DO  - https://doi.org/10.7494/OpMath.202610121
UR  - https://doi.org/10.7494/OpMath.202610121
AB  - 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.
KW  - Kirchhoff equation
KW  - Sobolev-critical exponent
KW  - normalized ground state
KW  - mountain-pass solution
SN  - 1232-9274
ER  -