Multiple normalized solutions for a quasi-linear Schrödinger equation via dual approach

Abstract

In this paper, we construct multiple normalized solutions of the following from quasi-linear Schrödinger equation: -\Delta u-\Delta(|u|^{2})u-\mu 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.