Normalized solutions for the NLS equation with potential in higher dimension: the purely Sobolev critical case
Analysis of PDEs
2025-08-01 v1
Abstract
We study normalized solutions for the nonlinear Schrodinger (NLS) equation with potential and Sobolev critical nonlinearity. By establishing suitable assumptions on the potential, together with new techniques, we find a mountain-pass type solution for N>=6, which solves an open problem presented in a recent paper [Verzini and Yu, arXiv:2505.05357v1]. Moreover, we also find a local minimizer with negative energy for N>=3, which improves the results in [Verzini and Yu, arXiv:2505.05357v1].
Keywords
Cite
@article{arxiv.2507.23639,
title = {Normalized solutions for the NLS equation with potential in higher dimension: the purely Sobolev critical case},
author = {Juntao Sun and Shuai Yao and He Zhang},
journal= {arXiv preprint arXiv:2507.23639},
year = {2025}
}