Existence of normalized ground states for supercritical/critical NLS with a partial confinement
Abstract
This paper is devoted to the existence of normalized ground states for a mass supercritical/critical nonlinear Schrödinger equation with a partial confinement. In particular, we extend the main result of J. Bellazzini, N. Boussaid, L. Jeanjean, and N. Visciglia [Comm. Math. Phys. 353 (2017), pp. 229–251] with a simpler proof and the improvement lies in the fact that we obtain here an explicit bound c 0 c_0 (or c 1 c_1 ) which guarantees that when 0 > c > c 0 0 > c > c_0 (or 0 > c > c 1 0 > c > c_1 ) there exists a normalized ground state whose L 2 L^2 norm is c \sqrt {c} , and that we treat the mass critical case.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 6
- Pages
- 2421–2431
- Publication date
- 28 January 2026
- Language
- EN