| 非标准增长椭圆型方程整解的Liouville型定理 |
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| 引用本文： | 梁廷. 非标准增长椭圆型方程整解的Liouville型定理[J]. 洛阳师范学院学报, 1996, 0(2) |
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| 作者姓名： | 梁廷 |
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| 作者单位： | 中山大学数学系!广州510275 |
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| 摘 要： | 在整个n维空间上考虑非标准增长椭圆型方程（1），证明如果存在某个适当的α＞0，使（1）的解u∈La（En），那么u只能是零解．
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| 关 键 词： | 椭圆型方程 非标准增长条件 各向异性Sobolev空间 广义解 整解 零解 |
A Liouville type Theorem for Entire Solutions of Elliptic Equations with Non Standard Growth Conditions |
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| Liang Xiting. A Liouville type Theorem for Entire Solutions of Elliptic Equations with Non Standard Growth Conditions[J]. Journal of Luoyang Teachers College, 1996, 0(2) |
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| Authors: | Liang Xiting |
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| Abstract: | Consider on En the following equation: where Ai and B satisfy the structural conditions: where pi> 1, k≥1 and 1 - 1/p≥γi/pi=γ/p≤1-1/p* 1/n< (1/pi )/n= 1/p= l/p * + 1/m<1. It is proved that if (En) be a entire generalized solution of the equation and u∈ Lα (E),α>0 may be arbitrary for γ=p - 1 and for p-1<γ≤p (1 - 1/p * ),then, u must be a null solution. |
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| Keywords: | elliptic equation non standard growth condition anisotropic Sobolec space generalized solution entire solution null solution |
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