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Liouville Type Theorems for Solutions of Elliptic Equations
Author(s): LIANG (jijin)ting
Journal: ACADEMIC FORUM OF NAN DU(NATURAL SCIENCES EDITION), Year 2001 , Issue 3 , Page 1-7
Keyword:  椭圆型方程整解Liouville型定理;
Abstract: 在整个空间En上考虑下面的椭圆型方程:div A(x,u, u) + B(x,u, u)=O. 其中,ξ·A(x,u,ξ) ≥ |ξ|P,1 < p < n;|A(x,u,ξ)| ≤κ|ξ|P-1,k≥ 1; | B(x,u,ξ)|≤b(x)|ξ|γ,p-1≤γ<p.利用解的最大值原理作出未知解u在任意B(ρ)上最大值的估计式并由此证明了如下的Liouville型定理:方程的整解u一定是零解,倘若u∈Lα(En),α为某个适当常数.
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