Orbital Stability of Standing Waves for the Sobolev Critical Schrödinger Equation with Inverse-Power Potential
In this paper, we study the Cauchy problem for the nonlinear Schrödinger equation with focusing inverse-power potential and the Sobolev critical nonlinearity. By considering the corresponding local minimization problem, we show that the existence of ground state solutions. Then, we prove that the so...
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| Veröffentlicht in: | Qualitative theory of dynamical systems 2024-09, Vol.23 (4), Article 147 |
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| container_title | Qualitative theory of dynamical systems |
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| creator | Cao, Leijin Feng, Binhua Mo, Yichun |
| description | In this paper, we study the Cauchy problem for the nonlinear Schrödinger equation with focusing inverse-power potential and the Sobolev critical nonlinearity. By considering the corresponding local minimization problem, we show that the existence of ground state solutions. Then, we prove that the solution of this equation exists globally when the initial data
φ
sufficiently close to the ground states. Based on these results, we show that the set of ground states is orbitally stable. |
| doi_str_mv | 10.1007/s12346-024-00980-7 |
| format | Article |
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φ
sufficiently close to the ground states. Based on these results, we show that the set of ground states is orbitally stable.</description><identifier>ISSN: 1575-5460</identifier><identifier>EISSN: 1662-3592</identifier><identifier>DOI: 10.1007/s12346-024-00980-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Cauchy problems ; Difference and Functional Equations ; Dynamical Systems and Ergodic Theory ; Ground state ; Mathematics ; Mathematics and Statistics ; Nonlinearity ; Orbital stability ; Schrodinger equation ; Standing waves</subject><ispartof>Qualitative theory of dynamical systems, 2024-09, Vol.23 (4), Article 147</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-54814b14a4bef1483f4822efae366d020b1652d6ba649f6f7286a914bb0bea2e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12346-024-00980-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12346-024-00980-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Cao, Leijin</creatorcontrib><creatorcontrib>Feng, Binhua</creatorcontrib><creatorcontrib>Mo, Yichun</creatorcontrib><title>Orbital Stability of Standing Waves for the Sobolev Critical Schrödinger Equation with Inverse-Power Potential</title><title>Qualitative theory of dynamical systems</title><addtitle>Qual. Theory Dyn. Syst</addtitle><description>In this paper, we study the Cauchy problem for the nonlinear Schrödinger equation with focusing inverse-power potential and the Sobolev critical nonlinearity. By considering the corresponding local minimization problem, we show that the existence of ground state solutions. Then, we prove that the solution of this equation exists globally when the initial data
φ
sufficiently close to the ground states. Based on these results, we show that the set of ground states is orbitally stable.</description><subject>Cauchy problems</subject><subject>Difference and Functional Equations</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Ground state</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Orbital stability</subject><subject>Schrodinger equation</subject><subject>Standing waves</subject><issn>1575-5460</issn><issn>1662-3592</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsv4CrgOprbZKZLKVULhQpVXIZkmtiUcdImaUtfzBfwxcw4gjtX5xzO_53LD8A1wbcE4_IuEsq4QJhyhPGowqg8AQMiBEWsGNHTnBdlgQou8Dm4iHGNsaAlowPg50G7pBq4SEq7xqUj9LYr2qVr3-Gb2psIrQ8wrQxceO0bs4fj4JKrO6heha_PTmkCnGx3KjnfwoNLKzht9yZEg579IfeefTJtcqq5BGdWNdFc_cYheH2YvIyf0Gz-OB3fz1BNS5zypRXhmnDFtbGEV8zyilJjlWFCLDHFmoiCLoVWgo-ssCWthBplRGNtFDVsCG76uZvgtzsTk1z7XWjzSskwKTineUNW0V5VBx9jMFZugvtQ4SgJlp2xsjdWZmPlj7GyzBDroZjF3ed_o_-hvgG0xX0F</recordid><startdate>20240901</startdate><enddate>20240901</enddate><creator>Cao, Leijin</creator><creator>Feng, Binhua</creator><creator>Mo, Yichun</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240901</creationdate><title>Orbital Stability of Standing Waves for the Sobolev Critical Schrödinger Equation with Inverse-Power Potential</title><author>Cao, Leijin ; Feng, Binhua ; Mo, Yichun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-54814b14a4bef1483f4822efae366d020b1652d6ba649f6f7286a914bb0bea2e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Cauchy problems</topic><topic>Difference and Functional Equations</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Ground state</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Orbital stability</topic><topic>Schrodinger equation</topic><topic>Standing waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cao, Leijin</creatorcontrib><creatorcontrib>Feng, Binhua</creatorcontrib><creatorcontrib>Mo, Yichun</creatorcontrib><collection>CrossRef</collection><jtitle>Qualitative theory of dynamical systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cao, Leijin</au><au>Feng, Binhua</au><au>Mo, Yichun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Orbital Stability of Standing Waves for the Sobolev Critical Schrödinger Equation with Inverse-Power Potential</atitle><jtitle>Qualitative theory of dynamical systems</jtitle><stitle>Qual. Theory Dyn. Syst</stitle><date>2024-09-01</date><risdate>2024</risdate><volume>23</volume><issue>4</issue><artnum>147</artnum><issn>1575-5460</issn><eissn>1662-3592</eissn><abstract>In this paper, we study the Cauchy problem for the nonlinear Schrödinger equation with focusing inverse-power potential and the Sobolev critical nonlinearity. By considering the corresponding local minimization problem, we show that the existence of ground state solutions. Then, we prove that the solution of this equation exists globally when the initial data
φ
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| subjects | Cauchy problems Difference and Functional Equations Dynamical Systems and Ergodic Theory Ground state Mathematics Mathematics and Statistics Nonlinearity Orbital stability Schrodinger equation Standing waves |
| title | Orbital Stability of Standing Waves for the Sobolev Critical Schrödinger Equation with Inverse-Power Potential |
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