{"title":"度量图上非线性薛定谔方程峰值边界态的存在性和多重性","authors":"Haixia Chen, Simone Dovetta, Angela Pistoia, Enrico Serra","doi":"10.1088/1361-6544/ad5133","DOIUrl":null,"url":null,"abstract":"We establish existence and multiplicity of one-peaked and multi-peaked positive bound states for nonlinear Schrödinger equations on general compact and noncompact metric graphs. Precisely, we construct solutions concentrating at every vertex of odd degree greater than or equal to 3. We show that these solutions are not minimizers of the associated action and energy functionals. To the best of our knowledge, this is the first work exhibiting solutions concentrating at vertices with degree different than 1. The proof is based on a suitable Ljapunov–Schmidt reduction.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"32 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and multiplicity of peaked bound states for nonlinear Schrödinger equations on metric graphs\",\"authors\":\"Haixia Chen, Simone Dovetta, Angela Pistoia, Enrico Serra\",\"doi\":\"10.1088/1361-6544/ad5133\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish existence and multiplicity of one-peaked and multi-peaked positive bound states for nonlinear Schrödinger equations on general compact and noncompact metric graphs. Precisely, we construct solutions concentrating at every vertex of odd degree greater than or equal to 3. We show that these solutions are not minimizers of the associated action and energy functionals. To the best of our knowledge, this is the first work exhibiting solutions concentrating at vertices with degree different than 1. The proof is based on a suitable Ljapunov–Schmidt reduction.\",\"PeriodicalId\":54715,\"journal\":{\"name\":\"Nonlinearity\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-06-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinearity\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6544/ad5133\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinearity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6544/ad5133","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Existence and multiplicity of peaked bound states for nonlinear Schrödinger equations on metric graphs
We establish existence and multiplicity of one-peaked and multi-peaked positive bound states for nonlinear Schrödinger equations on general compact and noncompact metric graphs. Precisely, we construct solutions concentrating at every vertex of odd degree greater than or equal to 3. We show that these solutions are not minimizers of the associated action and energy functionals. To the best of our knowledge, this is the first work exhibiting solutions concentrating at vertices with degree different than 1. The proof is based on a suitable Ljapunov–Schmidt reduction.
期刊介绍:
Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest.
Subject coverage:
The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal.
Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena.
Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.