${\mathbb R}$$N$上一类Kirchhoff型方程径向对称正解的存在性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 142-148.

${\mathbb R}$^$N$上一类Kirchhoff型方程径向对称正解的存在性

邓义华()

衡阳师范学院数学与统计学院湖南衡阳 421002

收稿日期:2019-10-16 出版日期:2021-02-26 发布日期:2021-01-29
作者简介:邓义华, E-mail: dengchen4032@126.com
基金资助:
湖南省自然科学基金(14JJ2120);湖南省双一流应用特色学科(湘教通[2018]469);智能信息处理与应用湖南省重点实验室基金(2016TP1020)

Existence of Positive Radial Solution to a Class of Kirchhoff type Equation in ${\mathbb R}$^$N$

Yihua Deng()

College of Mathematics and Statistics, Hengyang Normal University, Hunan Hengyang 421002

Received:2019-10-16 Online:2021-02-26 Published:2021-01-29
Supported by:
the NSF of Hunan Province(14JJ2120);the Double Top Application Characteristic Discipline of Hunan Province(湘教通[2018]469);the Fund for Intelligent Information Processing and Application Key Laboratory of Hunan Province(2016TP1020)

摘要/Abstract

摘要：

该文讨论了一类能量泛函不属于$C^1$类的Kirchhoff型方程，这类方程与等离子体物理和激光传输理论有密切的联系.通过变量变换，该文首先将所讨论的方程变成了与之等价的能量泛函属于$C^1$类的方程.然后，通过构造合适的Banach空间，在适当的条件下运用变分方法证明了所讨论的方程存在径向对称正解.

关键词: Kirchhoff型方程, 径向对称正解, 变分方法, Banach空间

Abstract:

In this paper, we discuss a class of Kirchhoff type equation whose energy function may not be of $C^1$ class. This equation is closely related to plasma physics and theories for propagation of laser beams. Using a change of variables, we get a new equivalent equation whose energy function is of $C^1$ class. Using a suitable Banach space and variational method, we prove that there is a positive radial solution to the given equation under proper conditions.

Key words: Kirchhoff type equation, Positive radial solution, Variational method, Banach space

中图分类号:

O175.2

邓义华. ${\mathbb R}$^$N$上一类Kirchhoff型方程径向对称正解的存在性[J]. 数学物理学报, 2021, 41(1): 142-148.

Yihua Deng. Existence of Positive Radial Solution to a Class of Kirchhoff type Equation in ${\mathbb R}$^$N$[J]. Acta mathematica scientia,Series A, 2021, 41(1): 142-148.

参考文献 13

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