{"title":"通过全局分岔法实现具有一般非线性的薛定谔方程在有界域中的归一化解","authors":"Wei Ji","doi":"arxiv-2409.10299","DOIUrl":null,"url":null,"abstract":"We obtain the existence, nonexistence and multiplicity of positive solutions\nwith prescribed mass for nonlinear Schr\\\"{o}dinger equations in bounded domains\nvia a global bifurcation approach. The nonlinearities in this paper can be mass\nsupercritical, critical, subcritical or some mixes of these cases, and the\nequation can be autonomous or non-autonomous. This generalizes a result in\nNoris, Tavares and Verzini [\\emph{Anal. PDE}, 7 (8) (2014) 1807-1838], where\nthe equation is autonomous with homogeneous nonlinearities. Besides, we have\nproven some orbital stability or instability results.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach\",\"authors\":\"Wei Ji\",\"doi\":\"arxiv-2409.10299\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain the existence, nonexistence and multiplicity of positive solutions\\nwith prescribed mass for nonlinear Schr\\\\\\\"{o}dinger equations in bounded domains\\nvia a global bifurcation approach. The nonlinearities in this paper can be mass\\nsupercritical, critical, subcritical or some mixes of these cases, and the\\nequation can be autonomous or non-autonomous. This generalizes a result in\\nNoris, Tavares and Verzini [\\\\emph{Anal. PDE}, 7 (8) (2014) 1807-1838], where\\nthe equation is autonomous with homogeneous nonlinearities. Besides, we have\\nproven some orbital stability or instability results.\",\"PeriodicalId\":501165,\"journal\":{\"name\":\"arXiv - MATH - Analysis of PDEs\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10299\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10299","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach
We obtain the existence, nonexistence and multiplicity of positive solutions
with prescribed mass for nonlinear Schr\"{o}dinger equations in bounded domains
via a global bifurcation approach. The nonlinearities in this paper can be mass
supercritical, critical, subcritical or some mixes of these cases, and the
equation can be autonomous or non-autonomous. This generalizes a result in
Noris, Tavares and Verzini [\emph{Anal. PDE}, 7 (8) (2014) 1807-1838], where
the equation is autonomous with homogeneous nonlinearities. Besides, we have
proven some orbital stability or instability results.
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