含有Hénon项的非线性椭圆系统稳定解的Liouville定理  

Liouville theorems for stable solutions of a nonlinear elliptic system with Hénon term

作　　者：黄宇鑫 甘怡清 胡良根 HUANG Yuxin;GAN Yiqing;HU Lianggen(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China;Yaojiang Middle School,Yuyao 315400,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211 [2]姚江中学,浙江余姚315400

出　　处：《宁波大学学报（理工版）》2024年第2期86-95,共10页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：宁波市自然科学基金(2023J127).

摘　　要：本文主要研究含有Hénon项的k-耦合椭圆系统-Δu_(i)=Σ_(j-1)^(k)β_(ij)|χ|^(α)|u_(i)|^(q-1)ui|uj|^(q+1),x∈R^(N)其中k是一个固定的正整数,i=1,2,…,k,q≥1,N≥3,B=(β_(ij))_(i,j=1)^(k)为实对称矩阵.首先使用Pohozaev恒等式构造单调公式,并发现其等价关系.当矩阵B严格余正时,联合使用Pohozaev恒等式、单调公式和爆缩序列方法证明了(无论是正的还是变号的)稳定解的Liouville定理.In this paper,we focus on the k-coupled elliptic system with Hénon term -Δu_(i)=Σ_(j-1)^(k)β_(ij)|χ|^(α)|u_(i)|^(q-1)ui|uj|^(q+1),x∈R^(N),where k is a fixed positive integer i=1,2,…,k,q≥1,N≥3,B=(β_(ij))_(i,j=1)^(k) a real symmetric matrix.We first use Pohozaev identity to construct monotonicity formula and find their equivalent relation.For the case that the matrix B is strictly co-positive,we obtain Liouville theorems of stable solutions(whether positive or sign-changing),by the use of Pohozaev identity,monotonicity formula of solution together with a blowing down sequence.

关 键 词：LIOUVILLE定理 稳定解 POHOZAEV恒等式 单调公式 爆缩序列 

分 类 号：O186[理学—数学]