外域中高阶Lane-Emden系统的Liouville型定理

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2022-03-16 DOI:10.1142/s0219199722500067

Yuxia Guo, Shaolong Peng

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引用次数: 1

摘要

在本文中，我们主要关注外部域中的以下系统：[公式：参见文本]，其中[公式：见文本]，[公式：查看文本]是整数，[公式，见文本]和[公式，参见文本]是多调和算子。我们证明了[公式：见正文]如果[公式：看正文]，和[公式：见正文]如果[公式：见文本]，上述系统的正解不存在。这篇论文的新颖之处在于，我们不要求[公式：见正文]在无穷大处满足任何对称性和渐近条件。通过证明解的超调和性质，我们建立了偏微分方程组（PDE）和积分方程组（IE）之间的等价性，然后可以应用积分形式的标度球方法来证明解的不存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Liouville-type theorems for higher-order Lane–Emden system in exterior domains

In this paper, we are mainly concerned with the following system in an exterior domains: [Formula: see text] where [Formula: see text], [Formula: see text] is an integer, [Formula: see text], and [Formula: see text] is the polyharmonic operator. We prove the nonexistence of positive solutions to the above system for [Formula: see text] if [Formula: see text], and [Formula: see text] if [Formula: see text]. The novelty of the paper is that we do not ask [Formula: see text] satisfy any symmetry and asymptotic conditions at infinity. By proving the superharmonic properties of the solutions, we establish the equivalence between systems of partial differential equations (PDEs) and integral equations (IEs), then the method of scaling sphere in integral form can be applied to prove the nonexistence of the solutions.

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来源期刊

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.