Multiple normalized solutions for a quasi-linear Schrödinger equation via dual approach - Zhang, Lin; Li, Yongqing; Wang, Zhi-Qiang (Topological Methods in Nonlinear Analysis, 2023)
In this paper, we construct multiple normalized solutions of the following from quasi-linear Schrödinger equation:-Δ u-Δ(|u|^{2})u-μ u=|u|^{p-2}u, \quad\text{in } \mathbb{R}^N,subject to a mass-subcritical constraint. In order to overcome non-smoothness of the associated variational formulation we make use of the dual approach.The constructed solutions possess energies being clustered at $0$ level which makes it difficult to use existing methods for non-smooth variational problems such as the variational perturbation approach.