Kirchhoff方程单峰解的局部唯一性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 432-440.

Kirchhoff方程单峰解的局部唯一性

许诗敏(),王春花()

^{华中师范大学数学与统计学学院武汉 430079}

收稿日期:2018-09-05 出版日期:2020-04-26 发布日期:2020-05-21
作者简介:许诗敏, E-mail:xushiminxsm@163.com|王春花, E-mail:chunhuawang@mail.ccnu.edu.cn
基金资助:
国家自然科学基金(11671162)

Local Uniqueness of a Single Peak Solution of a Subcritical Kirchhoff Problem in R³

Shimin Xu(),Chunhua Wang()

^{School of Mathematics and Statistics, Central China Normal University, Wuhan 430079}

Received:2018-09-05 Online:2020-04-26 Published:2020-05-21
Supported by:
国家自然科学基金(11671162)

摘要/Abstract

摘要：

该文主要证明了以下非线Kirchhoff问题的单峰解的局部唯一性

$-\Big(\epsilon^2 a+ \epsilon b \int_{\mathbb{R} ^3} |\nabla u|^2{\rm d}x\Big) \Delta u + u=K(x)|u|^{p-1}u, u>0,x \in \mathbb{R} ^3,$

其中ε>0任意小，a，b>0，1 < p < 5，K：$\mathbb{R}^3$→$\mathbb{R}$是连续有界函数.该文主要采用反证法结合局部的Pohozeav恒等式进行证明.

关键词: 非线性Kirchhoff问题, 局部唯一性, Pohozaev恒等式

Abstract:

In this paper, we obtain the local uniqueness of a single peak solution to the following Kirchhoff problem

$-\Big(\epsilon^2 a+ \epsilon b \int_{\mathbb{R} ^3} |\nabla u|^2{\rm d}x\Big) \Delta u + u=K(x)|u|^{p-1}u, u>0,x \in \mathbb{R} ^3,$

for ε>0 sufficiently small, where a, b>0 and 1 < p < 5 are constants, K: $\mathbb{R}^3$→$\mathbb{R}$ isabounded continuous function. We mainly use a contradiction argument developed by Li G, Luo P, Peng S in[20], applying some local pohozaev identities. Our result is totally new for Kirchhoff equations.

Key words: Local uniqueness, Nonlinear Kirchhoff equations, Pohozaev identities

中图分类号:

O175.2

许诗敏,王春花. Kirchhoff方程单峰解的局部唯一性[J]. 数学物理学报, 2020, 40(2): 432-440.

Shimin Xu,Chunhua Wang. Local Uniqueness of a Single Peak Solution of a Subcritical Kirchhoff Problem in R³[J]. Acta mathematica scientia,Series A, 2020, 40(2): 432-440.

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