一类退化椭圆型方程的多重性结果和全局分岔

Nonlinear Analysis and Differential Equations Pub Date : 1900-01-01 DOI:10.12988/NADE.2014.3615

M. Amattat

{"title":"一类退化椭圆型方程的多重性结果和全局分岔","authors":"M. Amattat","doi":"10.12988/NADE.2014.3615","DOIUrl":null,"url":null,"abstract":"We consider the question of determining the exact number of solutions of the problem E p λ below We distinguish two cases: whether 1 <p � 2o r 2 <p< ∞ . In the first case, we shall show that the problem E p behaves like in the semi-linear case which corresponds to p = 2.. In the second case and under some conditions which will be specified later; we shall show that the spectrum for problem E p consists of a collection of intervals In ,n =1 , 2, 3, whose ends points are members of the sequences (λn)n ,( μn)n where the first one is the sequence of eigenvalues for the pseudo-Laplacian operator and the other one is a sequence of a kind of eigenvalues for E p . And each time λ = μn, there exists secondary bifurcating continuum en of singular solutions which are diffeomorphic to [0 ,π ] n ,n =1 , 2..","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multiplicity Results and Global Bifurcations for a Degenerate Elliptic Equation\",\"authors\":\"M. Amattat\",\"doi\":\"10.12988/NADE.2014.3615\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the question of determining the exact number of solutions of the problem E p λ below We distinguish two cases: whether 1 <p � 2o r 2 <p< ∞ . In the first case, we shall show that the problem E p behaves like in the semi-linear case which corresponds to p = 2.. In the second case and under some conditions which will be specified later; we shall show that the spectrum for problem E p consists of a collection of intervals In ,n =1 , 2, 3, whose ends points are members of the sequences (λn)n ,( μn)n where the first one is the sequence of eigenvalues for the pseudo-Laplacian operator and the other one is a sequence of a kind of eigenvalues for E p . And each time λ = μn, there exists secondary bifurcating continuum en of singular solutions which are diffeomorphic to [0 ,π ] n ,n =1 , 2..\",\"PeriodicalId\":315586,\"journal\":{\"name\":\"Nonlinear Analysis and Differential Equations\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis and Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/NADE.2014.3615\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis and Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/NADE.2014.3615","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}