Kirchhoff方程规范解的存在性

徐麟; 谢启林

doi:10.12052/gdutxb.240013

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Kirchhoff方程规范解的存在性

微分方程及其应用 | 更新时间：2026-05-27

- Kirchhoff方程规范解的存在性
- The Existence of Normalized Solutions for Kirchhoff Equation
- 广东工业大学学报 2024年41卷第5期页码：125-128
- 作者机构：
  
  广东工业大学数学与统计学院,广东,广州,510006
- 作者简介：
  
  徐麟(1999–) ，男，硕士研究生，主要研究方向为非线性泛函分析，E-mail：xl1244176808@163.com
  谢启林(1989–) ，男，副教授，博士，硕士研究生导师，主要研究方向为非线性泛函分析，E-mail：xieql@gdut.edu.cn
- 基金信息：
  
  广东省自然科学基金资助项目(2021A1515010383，2022A1515010644)
- DOI：10.12052/gdutxb.240013
  中图分类号： O177
- 纸质出版：2024
- 稿件说明：
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徐麟, 谢启林. Kirchhoff方程规范解的存在性[J]. 广东工业大学学报, 2024, 41(5): 125-128.

Xu Lin, Xie Qi-lin. The Existence of Normalized Solutions for Kirchhoff Equation[J]. 2024, 41(5): 125-128.
徐麟, 谢启林. Kirchhoff方程规范解的存在性[J]. 广东工业大学学报, 2024, 41(5): 125-128. DOI： 10.12052/gdutxb.240013.

Xu Lin, Xie Qi-lin. The Existence of Normalized Solutions for Kirchhoff Equation[J]. 2024, 41(5): 125-128. DOI： 10.12052/gdutxb.240013.

摘要

由于Kirchhoff方程在众多物理问题中有着十分重要的应用，其规范解问题在近年来逐渐引起大批学者的研究兴趣。这些研究集中于探讨方程规范解的存在性问题，即在特定质量约束条件下，是否能找到满足方程的解。文章研究了一类带组合非线性项Kirchhoff方程规范解的存在性问题。通过利用变分法中的极小化方法，集中紧性原理和消失引理，证明了在扩散情形下对任意质量约束，方程存在一个规范解。对比已有的结果，文章的结论是对已有相关结果的推广。

Abstract

Due to the significant applications of the Kirchhoff equation in numerous physical problems

the issue of normalized solutions has gradually attracted the research interest of a large number of scholars in recent years. These studies focus on exploring the existence of normalized solutions to equations

specifically

whether solutions that satisfy the equations can be found under certain mass constraint conditions. An investigation is conducted into the existence of normalized solutions for a class of Kirchhoff equations with combined nonlinear terms. By utilizing the minimization method in variational calculus

along with the concentration compactness principle and the vanishing lemma

it has been proven that under diffusion conditions with arbitrary mass constraints

the equation possesses a normalized solution. Comparing with existing results

the conclusions of the research serve as an extension of existing related results.

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references

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