带椭球势阱的Kirchhoff型方程的变分问题

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1323-1333.

带椭球势阱的Kirchhoff型方程的变分问题

李容星(),王文清(),曾小雨*()

武汉理工大学数学科学研究中心武汉 430070

收稿日期:2019-01-03 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 曾小雨 E-mail:1436538761@qq.com;1923226881@qq.com;xyzeng@whut.edu.cn
作者简介:李容星, E-mail: 1436538761@qq.com|王文清, E-mail: 1923226881@qq.com
基金资助:
国家自然科学基金(11871387);国家自然科学基金(11601173);中央高校基本科研业务费专项基金(WUT：2019IB009);中央高校基本科研业务费专项基金(2019IB084)

A Constrained Variational Problem of Kirchhoff Type Equation with Ellipsoid-Shaped Potential

Rongxing Li(),Wenqing Wang(),Xiaoyu Zeng*()

Center of Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070

Received:2019-01-03 Online:2019-12-26 Published:2019-12-28
Contact: Xiaoyu Zeng E-mail:1436538761@qq.com;1923226881@qq.com;xyzeng@whut.edu.cn
Supported by:
the NSFC(11871387);the NSFC(11601173);the Fundamental Research Funds for the Central Universities(WUT：2019IB009);the Fundamental Research Funds for the Central Universities(2019IB084)

摘要/Abstract

摘要：

该文研究了一种具有特殊势阱的Kirchhoff椭圆方程的变分问题.这里势阱的底部为一个椭球.当相关参数趋向于某个临界值时，该文讨论了该变分问题解的渐近行为并证明了变分问题的解会在势阱底部椭球长轴的端点处发生爆破.

关键词: 约束变分法, 能量估计, Kirchhoff泛函, 椭圆方程

Abstract:

In this paper, we are considered with a constrained variational problem for certain type of Kirchhoff equation with trapping potential and the bottom of the potential is an ellipsoid. We are interested in the asymptotic behavior of solutions of variational problem and we prove that the minimizers of the minimization problem blows up at one of the endpoints of the major axis of the ellipsoid as the related parameter approaches a critical value.

Key words: Constraint variational method, Energy estimates, Kirchhoff functional, Elliptic equation

中图分类号:

O175.2

李容星,王文清,曾小雨. 带椭球势阱的Kirchhoff型方程的变分问题[J]. 数学物理学报, 2019, 39(6): 1323-1333.

Rongxing Li,Wenqing Wang,Xiaoyu Zeng. A Constrained Variational Problem of Kirchhoff Type Equation with Ellipsoid-Shaped Potential[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1323-1333.

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