{"title":"具有临界增长的双相基尔霍夫型问题正解的多重性和集中性","authors":"Jie Yang, Lintao Liu, Fengjuan Meng","doi":"10.12775/tmna.2023.026","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to study the multiplicity and concentration\nof positive solutions to the $(p,q)$ Kirchhoff-type problems\ninvolving a positive potential and a continuous nonlinearity with critical growth\nat infinity. Applying penalization techniques, truncation methods and the\nLusternik-Schnirelmann theory, we investigate a relationship between\n the number of positive solutions\nand the topology of the set where the potential $V$ attains its minimum values.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multiplicity and concentration of positive solutions to the double phase Kirchhoff type problems with critical growth\",\"authors\":\"Jie Yang, Lintao Liu, Fengjuan Meng\",\"doi\":\"10.12775/tmna.2023.026\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this paper is to study the multiplicity and concentration\\nof positive solutions to the $(p,q)$ Kirchhoff-type problems\\ninvolving a positive potential and a continuous nonlinearity with critical growth\\nat infinity. Applying penalization techniques, truncation methods and the\\nLusternik-Schnirelmann theory, we investigate a relationship between\\n the number of positive solutions\\nand the topology of the set where the potential $V$ attains its minimum values.\",\"PeriodicalId\":23130,\"journal\":{\"name\":\"Topological Methods in Nonlinear Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-03-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topological Methods in Nonlinear Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.12775/tmna.2023.026\",\"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":"Topological Methods in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12775/tmna.2023.026","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Multiplicity and concentration of positive solutions to the double phase Kirchhoff type problems with critical growth
The aim of this paper is to study the multiplicity and concentration
of positive solutions to the $(p,q)$ Kirchhoff-type problems
involving a positive potential and a continuous nonlinearity with critical growth
at infinity. Applying penalization techniques, truncation methods and the
Lusternik-Schnirelmann theory, we investigate a relationship between
the number of positive solutions
and the topology of the set where the potential $V$ attains its minimum values.
期刊介绍：
Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.
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