ON RADIALITY OF MINIMIZERS TO $L^2$ SUPERCRITICAL SCHRÖDINGER POISSON EQUATIONS WITH GENERAL NONLINEARITIES

doi:10.1007/s10473-025-0222-7

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (2): 684-694.doi: 10.1007/s10473-025-0222-7

ON RADIALITY OF MINIMIZERS TO $L^2$ SUPERCRITICAL SCHRÖDINGER POISSON EQUATIONS WITH GENERAL NONLINEARITIES

Chengcheng Wu¹, Linjie Song²

1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2023-09-09 修回日期:2024-09-25 出版日期:2025-03-25 发布日期:2025-05-08

ON RADIALITY OF MINIMIZERS TO $L^2$ SUPERCRITICAL SCHRÖDINGER POISSON EQUATIONS WITH GENERAL NONLINEARITIES

Chengcheng Wu¹, Linjie Song²

1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2023-09-09 Revised:2024-09-25 Online:2025-03-25 Published:2025-05-08
About author:Chengcheng Wu, E-mail: wuchengcheng@amss.ac.cn;Linjie Song, E-mail: songlinjie@mail.tsinghua.edu.cn
Supported by:
Wu's research was supported by the NSFC (12031015); Song's research was supported by the Shuimu Tsinghua Scholar Program, the National Funded Postdoctoral Research Program (GZB20230368) and the China Postdoctoral Science Foundation (2024T170452).

摘要/Abstract

摘要： We investigate the radial symmetry of minimizers on the Pohozaev-Nehari manifold to the Schrödinger Poisson equation with a general nonlinearity $f(u)$. Particularly, we allow that $f$ is $L^2$ supercritical. The main result shows that minimizers are radially symmetric modulo suitable translations.

关键词: Schrödinger-Poisson equations, radial symmetry, Pohozaev-Nehari manifold

Abstract: We investigate the radial symmetry of minimizers on the Pohozaev-Nehari manifold to the Schrödinger Poisson equation with a general nonlinearity $f(u)$. Particularly, we allow that $f$ is $L^2$ supercritical. The main result shows that minimizers are radially symmetric modulo suitable translations.

Key words: Schrödinger-Poisson equations, radial symmetry, Pohozaev-Nehari manifold

中图分类号:

35Q55

Chengcheng Wu, Linjie Song. ON RADIALITY OF MINIMIZERS TO $L^2$ SUPERCRITICAL SCHRÖDINGER POISSON EQUATIONS WITH GENERAL NONLINEARITIES[J]. 数学物理学报(英文版), 2025, 45(2): 684-694.

Chengcheng Wu, Linjie Song. ON RADIALITY OF MINIMIZERS TO $L^2$ SUPERCRITICAL SCHRÖDINGER POISSON EQUATIONS WITH GENERAL NONLINEARITIES[J]. Acta mathematica scientia,Series B, 2025, 45(2): 684-694.

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ON RADIALITY OF MINIMIZERS TO $L^2$ SUPERCRITICAL SCHRÖDINGER POISSON EQUATIONS WITH GENERAL NONLINEARITIES

ON RADIALITY OF MINIMIZERS TO $L^2$ SUPERCRITICAL SCHRÖDINGER POISSON EQUATIONS WITH GENERAL NONLINEARITIES

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