Non-radial normalized solutions for a nonlinear Schrodinger equation
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Date
2023-02-27
Authors
Tong, Zhi-Juan
Chen, Jianqing
Wang, Zhi-Qiang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the existence of multiple non-radial positive solutions of the L2-constrained problem
-Δu - Q(ɛx)|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 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.
Description
Keywords
Symmetry breaking, Local minimizer, Concentration, Nonlinear Schrödinger equations
Citation
Tong, Z. J., Chen, J., & Wang, Z. Q. (2023). Non-radial normalized solutions for a nonlinear Schrodinger equation. <i>Electronic Journal of Differential Equations, 2023</i>(19), pp. 1-14.