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
{"title":"外域中高阶Lane-Emden系统的Liouville型定理","authors":"Yuxia Guo, Shaolong Peng","doi":"10.1142/s0219199722500067","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Liouville-type theorems for higher-order Lane–Emden system in exterior domains\",\"authors\":\"Yuxia Guo, Shaolong Peng\",\"doi\":\"10.1142/s0219199722500067\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":50660,\"journal\":{\"name\":\"Communications in Contemporary Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Contemporary Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219199722500067\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Contemporary Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219199722500067","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
2.90
自引率
6.20%
发文量
78
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.
期刊最新文献
Maximal directional derivatives in Laakso space Smooth modules over the N = 1 Bondi–Metzner–Sachs superalgebra Pseudoconvex submanifolds in Kähler 4-manifolds A characterization of the subspace of radially symmetric functions in Sobolev spaces A moment map for the variety of Jordan algebras
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1