{"title":"具有至少质量临界非线性的schrÖdinger方程归一化基态的注释","authors":"Yanyan Liu, Leiga Zhao","doi":"10.11948/20230139","DOIUrl":null,"url":null,"abstract":"We are concerned with the nonlinear Schrödinger equation <p class=\"disp_formula\">$ \\begin{equation*}-\\Delta u+\\lambda u=g(u)\\text{ in }\\mathbb{R}^{N}\\text{, }\\lambda \\in\\mathbb{R}, \\end{equation*} $ with prescribed <inline-formula><tex-math id=\"M1\">\\begin{document}$L^{2}$\\end{document}</tex-math></inline-formula>-norm <inline-formula><tex-math id=\"M2\">\\begin{document}$\\int_{\\mathbb{R}^{N}}u^{2}dx=\\rho ^{2}$\\end{document}</tex-math></inline-formula>. Under general assumptions about the nonlinearity which allows at least mass critical growth, we prove the existence of a ground state solution to the problem via a clear constrained minimization method.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"56 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"REMARKS ON NORMALIZED GROUND STATES OF SCHRÖDINGER EQUATION WITH AT LEAST MASS CRITICAL NONLINEARITY\",\"authors\":\"Yanyan Liu, Leiga Zhao\",\"doi\":\"10.11948/20230139\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We are concerned with the nonlinear Schrödinger equation <p class=\\\"disp_formula\\\">$ \\\\begin{equation*}-\\\\Delta u+\\\\lambda u=g(u)\\\\text{ in }\\\\mathbb{R}^{N}\\\\text{, }\\\\lambda \\\\in\\\\mathbb{R}, \\\\end{equation*} $ with prescribed <inline-formula><tex-math id=\\\"M1\\\">\\\\begin{document}$L^{2}$\\\\end{document}</tex-math></inline-formula>-norm <inline-formula><tex-math id=\\\"M2\\\">\\\\begin{document}$\\\\int_{\\\\mathbb{R}^{N}}u^{2}dx=\\\\rho ^{2}$\\\\end{document}</tex-math></inline-formula>. Under general assumptions about the nonlinearity which allows at least mass critical growth, we prove the existence of a ground state solution to the problem via a clear constrained minimization method.\",\"PeriodicalId\":48811,\"journal\":{\"name\":\"Journal of Applied Analysis and Computation\",\"volume\":\"56 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Analysis and Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11948/20230139\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Analysis and Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11948/20230139","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
We are concerned with the nonlinear Schrödinger equation $ \begin{equation*}-\Delta u+\lambda u=g(u)\text{ in }\mathbb{R}^{N}\text{, }\lambda \in\mathbb{R}, \end{equation*} $ with prescribed \begin{document}$L^{2}$\end{document}-norm \begin{document}$\int_{\mathbb{R}^{N}}u^{2}dx=\rho ^{2}$\end{document}. Under general assumptions about the nonlinearity which allows at least mass critical growth, we prove the existence of a ground state solution to the problem via a clear constrained minimization method.
REMARKS ON NORMALIZED GROUND STATES OF SCHRÖDINGER EQUATION WITH AT LEAST MASS CRITICAL NONLINEARITY
We are concerned with the nonlinear Schrödinger equation
$ \begin{equation*}-\Delta u+\lambda u=g(u)\text{ in }\mathbb{R}^{N}\text{, }\lambda \in\mathbb{R}, \end{equation*} $ with prescribed \begin{document}$L^{2}$\end{document}-norm \begin{document}$\int_{\mathbb{R}^{N}}u^{2}dx=\rho ^{2}$\end{document}. Under general assumptions about the nonlinearity which allows at least mass critical growth, we prove the existence of a ground state solution to the problem via a clear constrained minimization method.
期刊介绍：
The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.
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