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-2u, in 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.