{"title":"Multiplicity of nontrivial solutions for a class of fractional elliptic equations","authors":"T. Kenzizi","doi":"10.1216/jie.2021.33.315","DOIUrl":null,"url":null,"abstract":"In this paper, we are concerned with the following fractional Laplacian equation (−∆)u = a(x)|u(x)|q−2u(x) + λb(x)|u(x)|p−2u(x) in (−1, 1), u > 0 in (−1, 1), u = 0 in R (−1, 1), where s ∈ (0, 1), λ > 0. Using variational methods, we show existence and multiplicity of positive solutions.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Integral Equations and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1216/jie.2021.33.315","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: 1
Abstract
In this paper, we are concerned with the following fractional Laplacian equation (−∆)u = a(x)|u(x)|q−2u(x) + λb(x)|u(x)|p−2u(x) in (−1, 1), u > 0 in (−1, 1), u = 0 in R (−1, 1), where s ∈ (0, 1), λ > 0. Using variational methods, we show existence and multiplicity of positive solutions.
期刊介绍：
Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications.
The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field.
The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.
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