Uniqueness of Single Peak Solutions for a Kirchhoff Equation

被引：0
|
作者：
Lv, Junhao [1 ]
Yi, Shichao [1 ,2 ]
Sun, Bo [1 ]
机构：
[1] Jiangsu Univ Sci & Technol, Sch Sci, Zhenjiang 212003, Peoples R China
[2] Yangzijiang Shipbldg Grp, Taizhou 212299, Peoples R China
来源：
MATHEMATICS | 2024年 / 12卷 / 10期
关键词：
Kirchhoff equations; single-peak solutions; uniqueness; Pohozaev identity; BOUND-STATES;
D O I：
10.3390/math12101462
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We deal with the following singular perturbation Kirchhoff equation: - (& varepsilon;(2)a + & varepsilon;b integral(3)(R)|del u|(2)dy) Delta u + Q(y)u = |u|(p-1)u, u is an element of H-1 (R-3), where constants a, b, epsilon > 0 and 1 < p < 5. In this paper, we prove the uniqueness of the concentrated solutions under some suitable assumptions on a symptotic behaviors of Q(y)and its first derivatives by using a type of Pohozaev identity for a small enough epsilon.To some extent, our result exhibits a new phenomenon for a kind of Q(x) which allows for different orders in different directions
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页数：7
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