类渐近线性p&q-Laplace方程弱解的全局衰减性

数学物理学报 ›› 2009, Vol. 29 ›› Issue (2): 217-222.

• 论文 • 下一篇

类渐近线性p&q-Laplace方程弱解的全局衰减性

何成军, 李工宝

(1.中国科学院武汉物理与数学研究所武汉 |430071; 2.华中师范大学数学与统计学院武汉 430072)

收稿日期:2007-06-15 修回日期:2008-12-30 出版日期:2009-04-25 发布日期:2009-04-25
基金资助:
国家自然科学基金(10571069, 10631030)资助

The Decay of Weak Solution of Pseudo-asymptotic Linear p&q-Laplacian Equation on R^N

He Chengjun, Li Gongbao

(1.Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079)

Received:2007-06-15 Revised:2008-12-30 Online:2009-04-25 Published:2009-04-25
Supported by:
国家自然科学基金(10571069, 10631030)资助

摘要/Abstract

摘要：

该文研究椭圆型方程
{ Δ_pu+m|u|^p-2u-Δ_qu+n|u|^q-2u=g(x, u), x ∈ R^N,
u ∈ W^{1, p}(R^N) ∩ W^{1, q}(R^N)

弱解在全空间R^N上的衰减性, 其中m, n ≥ 0, N ≥ 3, 1 < q < p < N, g(x, u)关于u满足类渐近线性. 证明了该方程的
弱解在无穷远处关于|x|呈指数衰减性.

关键词: p&q-Laplace, 椭圆型方程, 解的衰减性

Abstract:

In this paper, the authors study the following equation

{ Δ_pu+m|u|^p-2u-Δ_qu+n|u|^q-2u=g(x, u), x ∈ R^N,
u ∈ W^{1, p}(R^N) ∩ W^{1, q}(R^N)

where m, n>0, N\ ≥ 3, 1 < q < p < N and g(x, u) satisfies some kind of asymptotic about u at infinity.
They prove that the solution of this equation decays exponentially aoubt |x| at infinity.

Key words: p&q-Laplace, Elliptic equation, Decay.

中图分类号:

35B65

何成军, 李工宝. 类渐近线性p&q-Laplace方程弱解的全局衰减性[J]. 数学物理学报, 2009, 29(2): 217-222.

HE Cheng-Jun, LI Gong-Bao. The Decay of Weak Solution of Pseudo-asymptotic Linear p&q-Laplacian Equation on R^N[J]. Acta mathematica scientia,Series A, 2009, 29(2): 217-222.

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类渐近线性p&q-Laplace方程弱解的全局衰减性

The Decay of Weak Solution of Pseudo-asymptotic Linear p&q-Laplacian Equation on R^N

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类渐近线性p&q-Laplace方程弱解的全局衰减性

The Decay of Weak Solution of Pseudo-asymptotic Linear p&q-Laplacian Equation on RN

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The Decay of Weak Solution of Pseudo-asymptotic Linear p&q-Laplacian Equation on R^N