Multiple normalized solutions for a quasi-linear Schrödinger equation via dual approach
DOI:
https://doi.org/10.12775/TMNA.2022.052Słowa kluczowe
Quasi-linear Schrödinger equations, normalized solutions, dual method, the minimax principleAbstrakt
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.Bibliografia
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Prawa autorskie (c) 2023 Lin Zhang, Yongqing Li, Zhi-Qiang Wang
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
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