Normalized solutions to the Kirchhoff equation with L2-subcritical or critical nonlinearities in R2

被引：1
|
作者：
Hu, Jiaqing [1 ]
Mao, Anmin [1 ]
机构：
[1] Qufu Normal Univ, Sch Math Sci, Shandong 273165, Peoples R China
来源：
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2024年 / 55卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Normalized solution; Kirchhoff equation; Minimizing method; POSITIVE SOLUTIONS; EXISTENCE; GROWTH;
D O I：
10.1007/s13226-023-00383-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the existence of normalized solutions to the Kirchhoff equation with L-2- subcritical or critical nonlinearities - (a + b integral R-2 |& nabla;u|(2)dx) delta u = lambda u + |u|(p-2)u + mu|u|(q-2)u in R-2,where a, b, mu > 0, 2 < q < p <= 6. By minimizing methods and the concentration compactness principle, we prove the existence and nonexistence of normalized solutions when (p, q) belongs to a certain domain in R-2, and discuss how mu affects the existence of normalized solutions. Our main results may be illustrated by the red areas and green areas shown in Figure 1. Our results partially extend the results of Soave (J. Differ. Equ. 2020).
引用
收藏
页码：508 / 512
页数：5
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