非标准增长拟线性椭圆型方程整解的性质

Behaviours for Entire Solutions of Quasilinear Elliptic Equations with Nonstandard Growth Conditions

在整个n维欧氏空间E^n上考虑方程:div(?)(x,u,(?)u)=B(x,u,(?)u).u∈E^n其中(?)(x,u,ξ)和B(x,u,ξ),关于ξ为非标准增长.证明如果存在适当的t>0使方程的广义整解u∈L_1(E^n),那么u只能是零解.这是标准增长椭圆方程整解相应结果的推广.

It is proved that the entire generalized solution of a quasilinear elliptic equation with anisotropic growth conditions must be a null solution provided it belongs to L,(E^(n)) for a proper t>0.