带椭球势阱的Kirchhoff型方程的变分问题

Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (6): 1323-1333.

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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)

Abstract

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

CLC Number:

O175.2

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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References

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

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