{"title":"具有对流项的奇异拟线性椭圆问题","authors":"U. Guarnotta","doi":"10.1063/5.0082998","DOIUrl":null,"url":null,"abstract":"In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations and systems, exhibiting both singular and convective reaction terms. The importance of boundary conditions (Dirichlet, Neumann, or Robin) is also discussed. Existence is achieved via sub-supersolution and truncation techniques, fixed point theory, nonlinear regularity, and set-valued analysis, while uniqueness and multiplicity are obtained by monotonicity arguments.","PeriodicalId":335959,"journal":{"name":"INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020","volume":"135 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Singular quasilinear elliptic problems with convection terms\",\"authors\":\"U. Guarnotta\",\"doi\":\"10.1063/5.0082998\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations and systems, exhibiting both singular and convective reaction terms. The importance of boundary conditions (Dirichlet, Neumann, or Robin) is also discussed. Existence is achieved via sub-supersolution and truncation techniques, fixed point theory, nonlinear regularity, and set-valued analysis, while uniqueness and multiplicity are obtained by monotonicity arguments.\",\"PeriodicalId\":335959,\"journal\":{\"name\":\"INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020\",\"volume\":\"135 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0082998\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/5.0082998","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Singular quasilinear elliptic problems with convection terms
In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations and systems, exhibiting both singular and convective reaction terms. The importance of boundary conditions (Dirichlet, Neumann, or Robin) is also discussed. Existence is achieved via sub-supersolution and truncation techniques, fixed point theory, nonlinear regularity, and set-valued analysis, while uniqueness and multiplicity are obtained by monotonicity arguments.