Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 19, pp. 1-14.

Title: Non-radial normalized solutions for a nonlinear Schrodinger equation
       
Authors: Zhi-Juan Tong (Fujian Normal Univ., Fuzhou, China)
         Jianqing Chen (Fujian Normal Univ., Fuzhou, China}
         Zhi-Qiang Wang (Fujian Normal Univ., Fuzhou, China}

Abstract: 
This article concerns the existence of multiple non-radial
positive solutions of the L<sup>2</sup>-constrained problem
$$\displaylines{ 
-\Delta{u}-Q(\varepsilon x)|u|^{p-2}u=\lambda{u},\quad \text{in }\mathbb{R}^N,\cr
 \int_{\mathbb{R}^N}|u|^2dx=1,
}$$
where Q(x) is a radially symmetric function, &epsilon;&gt;0 is a small parameter,
N&ge;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.