Electron. J. Differential Equations, Vol. 2023 (2023), No. 19, pp. 1-14.

Non-radial normalized solutions for a nonlinear Schrodinger equation

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 −Δu−Q(εx)|u|p−2u=λu,in RN,∫RN|u|2dx=1, where Q(x) is a radially symmetric function, ε>0 is a small parameter, N≥2, and p∈(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

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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

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