期刊论文

Li, Gongbao

英文

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

1078-0947

2020

40

5

2739-2766

10.3934/dcds.2020148

2010 Mathematics Subject Classification. Primary: 35J20, 35J25, 35J60. Key words and phrases. Nonlinear Schrödinger system, normalized solutions, stability, standing waves. The project is supported by National Natural Science Foundation of China(Grant No.11771166), Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University #IRT 17R46. H.F Jia is also supported by National Postdoctoral Science Foundation of China(Grant No.2019M662833). X. Luo is also supported by National Natural Science Foundation of China(Grant No.11901147). ∗ Corresponding author: Gongbao Li.

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In this article, we deal with the existence, qualitative and symmetry properties of normalized solutions to the following nonlinear Schrödinger system \begin{document}$ \begin{equation*} \begin{cases} -\Delta u+(x_{1}^{2}+x_{2}^{2})u = \lambda_{1}u+\mu_{1}u^{3}+\beta uv^{2}, &\quad x\in \mathbb{R}^3,\\ -\Delta v+(x_{1}^{2}+x_{2}^{2})v = \lambda_{2}v+\mu_{2}v^{3}+\beta u^{2}v, &\quad x\in \mathbb{R}^3, \end{cases} \end{equation*} $\end{document} where \begin{document}$ \mu_{i}>0 $\end{document} (\begin{document}$ i $\end{document} = ...