超临界拟线性海森堡铁丝链薛定谔方程

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 1073-1084.

超临界拟线性海森堡铁丝链薛定谔方程

王继研^*(),程永宽

华南理工大学数学学院广州 510640

收稿日期:2022-09-05 修回日期:2023-02-06 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 王继研 E-mail:2585823895@qq.com
基金资助:
广东省自然科学基金(2020A1515010338)

Quasilinear Schrödinger Equations for the Heisenberg Ferromagnetic Spin Chain with the Supercritical Growth

Wang Jiyan^*(),Cheng Yongkuan

Department of Mathematics, South China University of Technology, Guangzhou 510640

Received:2022-09-05 Revised:2023-02-06 Online:2023-08-26 Published:2023-07-03
Contact: Jiyan Wang E-mail:2585823895@qq.com
Supported by:
GBABRF(2020A1515010338)

摘要/Abstract

摘要：

该文考虑一类来自于海森堡铁丝链模型的拟线性薛定谔方程, 通过摄动方法、截断技巧以及变量替换证明了超临界情形下该方程有一族单参数慢速衰减的正解.

关键词: 拟线性薛定谔方程, 约化方法, 变量替换

Abstract:

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain. Based on the perturbative approach, the cut off technique and the change of variables, we prove that the existence of infinity many positive solutions with slow decaying $O \big (|x| ^{-\frac{2}{p-1}}\big )$ at infinity.

Key words: Schr?dinger equations, Perturbative approach, Change of variables

中图分类号:

O175.2

王继研,程永宽. 超临界拟线性海森堡铁丝链薛定谔方程[J]. 数学物理学报, 2023, 43(4): 1073-1084.

Wang Jiyan,Cheng Yongkuan. Quasilinear Schrödinger Equations for the Heisenberg Ferromagnetic Spin Chain with the Supercritical Growth[J]. Acta mathematica scientia,Series A, 2023, 43(4): 1073-1084.

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