期刊论文

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

中文

数学物理学报

1003-3998

2020

40

02

432-440

10.3969/j.issn.1003-3998.2020.02.014

国家自然科学基金（11671162）~~；

本校为第一机构

该文主要证明了以下非线Kirchhoff问题的单峰解的局部唯一性$$ - \left( {{ \in ^2}a + \in b\int_{{{\rm\mathbb{R}}^3}} {{{\left| {\nabla u} \right|}^2}{\rm{d}}x} } \right)\Delta u + u = K\left( x \right){\left| u \right|^{p - 1}}u,u > 0,x \in {{\rm\mathbb{R}}^3}$$其中$ \in > 0$0任意小,$a,b > 0,1 < p < 5,K:{{\rm\mathbb{R}}^3} \to {\rm\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.

In this paper, we obtain the local uniqueness of a single peak solution to the following Kirchhoff problem $$ - \left( {{ \in ^2}a + \in b\int_{{{\rm\mathbb{R}}^3}} {{{\left| {\nabla u} \right|}^2}{\rm{d}}x} } \right)\Delta u + u = K\left( x \right){\left| u \right|^{p - 1}}u,u > 0,x \in {{\rm\mathbb{R}}^3}$$ for $ \in > 0$ sufficiently small, where $a,b > 0$ and $1 < p < 5$ are constants, $K:{{\rm\mathbb{R}}^3} \to {\rm\mathbb{R}}$ is a bounded continuous function. We mainly use a contradiction argument developed by Li G, Luo P, Peng S in [20], applying some local p...