Zhi-Juan Tong, Jianqing Chen, Zhi-Qiang Wang
Abstract:
This article concerns the existence of multiple non-radial positive solutions of the L2-constrained problem $$\displaylines{-\Delta{u}-Q(\varepsilon x)|u|^{p-2}u=\lambda{u},\quad \text{in }\mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=1,}$$ where \(Q(x)\) is a radially symmetric function, ε>0 is a small parameter, \(N\geq 2\), and \(p \in (2, 2+4/N)\) is assumed to be mass sub-critical. We are interested in the symmetry breaking of the normalized solutions and we prove the existence of multiple non-radial positive solutions as local minimizers of the energy functional.
Submitted January 16, 2023 Published February 27, 2023.
Math Subject Classifications: 35J20, 35J60, 58E40.
Key Words: Symmetry breaking; local minimizer; concentration; nonlinear Schrodinger equations.
DOI: https://doi.org/10.58997/ejde.2023.19
Show me the PDF file (378 KB), TEX file for this article.
 |
Zhi-Juan Tong College of Mathematics and Statistics Fujian Normal University Fuzhou, 350117, China email: qsx20200630@student.fjnu.edu.cn |
|---|---|
 |
Jianqing Chen College of Mathematics and Statistics Fujian Normal University Fuzhou, 350117, China email: jqchen@fjnu.edu.cn |
 |
Zhi-Qiang Wang College of Mathematics and Statistics Fujian Normal University Fuzhou, 350117, China email: zhi-qiang.wang@usu.edu |
Return to the EJDE web page