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.
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收藏
页数：22
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