Existence and Asymptotics of Normalized Ground States for a Sobolev Critical Kirchhoff Equation

被引：48

作者：

Li, Quanqing ^{[1
]}

Nie, Jianjun ^{[2
]}

Zhang, Wen ^{[3
,4
]}

机构：

[1] Honghe Univ, Dept Math, Mengzi 661100, Yunnan, Peoples R China

[2] North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China

[3] Hunan Univ Technol & Business, Coll Sci, Changsha 410205, Hunan, Peoples R China

[4] Univ Craiova, Dept Math, Craiova 200585, Romania

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Normalized ground state solutions; Sobolev critical growth; Sobolev subcritical approximation method; BEHAVIOR;

D O I：

10.1007/s12220-022-01171-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we investigate the existence and asymptotic properties of normalized solutions for the following Kirchhoff-type equation with Sobolev critical growth { I-(a + b integral(3)(R) |del u|(2)dx)triangle u + lambda u = mu|u|(p-2)u + |u|(4)u, in R-3, (P) u > 0, integral(3)(R) |u|(2)dx = m(2), in R-3, where a, b, m, mu > 0 and14/3 < p < 6. With the aid of the Sobolev subcritical approximation method that is the first time used to consider mass constrained Kirchhoff-type problems, and Schwartz symmetrization rearrangements, we obtain the existence of normalized ground states. Moreover, the asymptotic behavior of these solutions is also studied.

引用

页数：22

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