{"title":"具有不确定权重的 (p(x),q(x)) 类似拉普拉契系统的多重性结果","authors":"Khaled Kefi, Chaima Nefzi","doi":"10.1515/gmj-2023-2107","DOIUrl":null,"url":null,"abstract":"Under some suitable conditions, we show that at least three weak solutions exist for a system of differential equations involving the <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>q</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2107_eq_0108.png\" /> <jats:tex-math>{(p(x),q(x))}</jats:tex-math> </jats:alternatives> </jats:inline-formula> Laplacian-like with indefinite weights. The proof is related to the Bonanno–Marano critical theorem (<jats:italic>Appl. Anal.</jats:italic> 89 (2010), 1–10).","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"124 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights\",\"authors\":\"Khaled Kefi, Chaima Nefzi\",\"doi\":\"10.1515/gmj-2023-2107\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Under some suitable conditions, we show that at least three weak solutions exist for a system of differential equations involving the <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mo stretchy=\\\"false\\\">(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\\\"false\\\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\\\"false\\\">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>q</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\\\"false\\\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\\\"false\\\">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=\\\"false\\\">)</m:mo> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2023-2107_eq_0108.png\\\" /> <jats:tex-math>{(p(x),q(x))}</jats:tex-math> </jats:alternatives> </jats:inline-formula> Laplacian-like with indefinite weights. The proof is related to the Bonanno–Marano critical theorem (<jats:italic>Appl. Anal.</jats:italic> 89 (2010), 1–10).\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":\"124 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2023-2107\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2023-2107","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在一些合适的条件下,我们证明了涉及 ( p ( x ) , q ( x ) ) 的微分方程系统至少存在三个弱解 {(p(x),q(x))} 的微分方程系统至少存在三个弱解。证明与 Bonanno-Marano 临界定理有关(Appl.89 (2010), 1-10).
Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights
Under some suitable conditions, we show that at least three weak solutions exist for a system of differential equations involving the (p(x),q(x)){(p(x),q(x))} Laplacian-like with indefinite weights. The proof is related to the Bonanno–Marano critical theorem (Appl. Anal. 89 (2010), 1–10).
期刊介绍:
The Georgian Mathematical Journal was founded by the Georgian National Academy of Sciences and A. Razmadze Mathematical Institute, and is jointly produced with De Gruyter. The concern of this international journal is the publication of research articles of best scientific standard in pure and applied mathematics. Special emphasis is put on the presentation of results obtained by Georgian mathematicians.