Nonradial normalized solutions for a quasilinear Schr\"{o}dinger equation via dual approach
Analysis of PDEs
2025-09-09 v1
Abstract
In this paper, we will utilize the dual method to construct multiple nonradial normalized solutions of the following quasilinear Schr\"{o}dinger equation: \begin{equation*} -\Delta u-\Delta(|u|^{2})u-\mu u=|u|^{p-2}u, \qquad in \quad \mathbb{R}^N, \end{equation*} subject to a mass-subcritical constraint. It should be emphasized that the nonradial result of this equation is new. Besides that, when considering the nonradial problem, it is necessary to construct a new workspace to ensure the compactness. Meanwhile, in this paper, we will expand on the method mentioned in TMNA.
Cite
@article{arxiv.2509.05557,
title = {Nonradial normalized solutions for a quasilinear Schr\"{o}dinger equation via dual approach},
author = {Lin Zhang},
journal= {arXiv preprint arXiv:2509.05557},
year = {2025}
}