{"title":"Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition","authors":"Weiwei Zhao, Xiaoling Shao, Changhui Hu, Zhiyu Cheng","doi":"10.1186/s13661-024-01831-9","DOIUrl":null,"url":null,"abstract":"We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmonic properties of the differential systems. This improves the results in (Complex Var. Elliptic Equ. 5:1436–1450, 2013) and (Abstr. Appl. Anal. 2014:593210, 2014).","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boundary Value Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13661-024-01831-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmonic properties of the differential systems. This improves the results in (Complex Var. Elliptic Equ. 5:1436–1450, 2013) and (Abstr. Appl. Anal. 2014:593210, 2014).
期刊介绍：
The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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