带 $L^2$-次临界一般非线性项的拟线性 Schrödinger 方程规范化解的存在性——献给李工宝教授 70 寿辰

数学物理学报 ›› 2025, Vol. 45 ›› Issue (6): 1907-1927.

带 $L^2$-次临界一般非线性项的拟线性 Schrödinger 方程规范化解的存在性——献给李工宝教授 70 寿辰

叶红雨()

武汉科技大学理学院武汉 430065

收稿日期:2025-04-28 修回日期:2025-08-21 出版日期:2025-12-26 发布日期:2025-11-18
作者简介:叶红雨,E-mail:yyeehongyu@163.com
基金资助:
湖北自然科学基金(JCZRYB202500183)

The Existence of Normalized Solutions for the Quasilinear Schrödinger Equations with $L^2$-Subcritical General Nonlinearity

Hongyu Ye()

College of Science, Wuhan University of Science and Technology, Wuhan 430065

Received:2025-04-28 Revised:2025-08-21 Online:2025-12-26 Published:2025-11-18
Supported by:
Hubei Provincial Natural Science Foundation(JCZRYB202500183)

摘要/Abstract

摘要：

该文研究了带一般 $L^2$-次临界非线性项的拟线性 Schrödinger 方程规范化解的存在性. 利用集中紧致原理、Schwartz 对称化技巧和形变伸缩方法, 该文证明了拟线性 Schrödinger 方程全局极小能量规范化解的存在性与不存在性、局部极小规范化解的存在性. 该文的主要结果可以看作是带齐次非线性项的拟线性 Schrödinger 方程规范化解存在性结果的一个推广.

关键词: $L^2$-次临界一般非线性项, 约束极小化方法, 规范化解, 存在性, 拟线性 Schrodinger 方程.

Abstract:

This paper studies the existence of normalized solutions for quasilinear Schrödinger equation with $L^2$-subcritical general nonlinearity. By using the compactness concentration principle, Schwartz symmetric technique and scaling method, this paper proves the existence and nonexistence of global least energy normalized solutions and the existence of local minimal normalized solutions. The main results can be viewed an extension of the results concerning about the existence of normalized solutions to the quasilinear equation with a pure power nonlinearity.

Key words: $L^2$-subcritical general nonlinearity, constrained minimization method, normalized solutions, existence, quasilinear Schrodinger equations

中图分类号:

O175.23

叶红雨. 带 $L^2$-次临界一般非线性项的拟线性 Schrödinger 方程规范化解的存在性——献给李工宝教授 70 寿辰[J]. 数学物理学报, 2025, 45(6): 1907-1927.

Hongyu Ye. The Existence of Normalized Solutions for the Quasilinear Schrödinger Equations with $L^2$-Subcritical General Nonlinearity[J]. Acta mathematica scientia,Series A, 2025, 45(6): 1907-1927.

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