{"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}
引用次数: 0
Abstract
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.