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arXiv · 2509.05557

Nonradial normalized solutions for a quasilinear Schr\"{o}dinger equation via dual approach

Lin Zhang
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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.

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Lin Zhang. 2025-09-06. Nonradial normalized solutions for a quasilinear Schr\"{o}dinger equation via dual approach. https://arxiv.org/abs/2509.05557

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