{"title":"Normalized ground states for general pseudo-relativistic Schrödinger equations","authors":"Haijun Luo, Dan Wu","doi":"10.1080/00036811.2020.1849631","DOIUrl":null,"url":null,"abstract":"ABSTRACT In this paper, we consider the pseudo-relativistic type Schrödinger equations with general nonlinearities. By studying the related constrained minimization problems, we obtain the existence of ground states via applying the concentration-compactness principle. Then some properties of the ground states have been discussed, including regularity, symmetry and etc. Furthermore, we prove that the set of minimizers is a stable set for the initial value problem of the equations, that is, a solution whose initial data is near the set will remain near it for all time.","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"101 1","pages":"3410 - 3431"},"PeriodicalIF":1.1000,"publicationDate":"2020-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00036811.2020.1849631","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00036811.2020.1849631","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 3
Abstract
ABSTRACT In this paper, we consider the pseudo-relativistic type Schrödinger equations with general nonlinearities. By studying the related constrained minimization problems, we obtain the existence of ground states via applying the concentration-compactness principle. Then some properties of the ground states have been discussed, including regularity, symmetry and etc. Furthermore, we prove that the set of minimizers is a stable set for the initial value problem of the equations, that is, a solution whose initial data is near the set will remain near it for all time.
期刊介绍：
Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal
General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.
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