In this paper,we focus on the k-coupled elliptic system with Hénon term-△ui=Σkj=1βij|x|α|ui|q-1ui|uj|q+1 in (R)N,where kis a fixed positive integer,i=1,2,…,k,q≥1,N≥3,and B=(βij)ki,j=1 is 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
Key words
Liouville theorem/stable solutions/Pohozaev identity/monotonicity formula/blowing down sequence
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