A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity
We prove the existence of solutions u for some semilinear elliptic vector-field equations on IR2 with a nonlinearity which is allowed to grow at infinity ‘nearly like a linear exponential’ in lul. In some cases a growth like exp(alulγ), a > 0 , 0 < γ < 2 , is allowed. This is achieved by in...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buchkapitel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 57 |
|---|---|
| container_issue | |
| container_start_page | 37 |
| container_title | |
| container_volume | |
| creator | Brüning, E. |
| description | We prove the existence of solutions u for some semilinear elliptic vector-field equations on IR2 with a nonlinearity which is allowed to grow at infinity ‘nearly like a linear exponential’ in lul. In some cases a growth like exp(alulγ), a > 0 , 0 < γ < 2 , is allowed.
This is achieved by introducing an appropriate space E of ‘à priori-solutions’ for which some important continuous imbeddings are proven replacing the well known Sobolev-imbeddings for the d ≥ 3-dimensional case. Then the standard variational method is applied. |
| doi_str_mv | 10.1007/BFb0025760 |
| format | Book Chapter |
| fullrecord | <record><control><sourceid>springer</sourceid><recordid>TN_cdi_springer_books_10_1007_BFb0025760</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>springer_books_10_1007_BFb0025760</sourcerecordid><originalsourceid>FETCH-springer_books_10_1007_BFb00257603</originalsourceid><addsrcrecordid>eNqVj71OAzEQhM2fxAXS8ARb0pjYnH8uJSAiHoD-dEn2wgbHG2yHiLfnoiCoqUaamW-kEeJGqzutlJ88zuZK3Vvv1IkYT31TW6OMa1xjTkWlnXbS1U6f_WZWT72356IaYCsbY9WlGOW8PowYoyuxfoDIBYEjZA67QhwzcA9lz3JJG4x5cLoAGTcUKGKXAEOgbaEFfOKicJI9YVgCfuy6I72n8ga5JI6rYTseKSpf1-Ki70LG8Y9eidvZ8-vTi8zbRHGFqZ0zv-dWq_bwtf37Wv-j-g2lHFZC</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>book_chapter</recordtype></control><display><type>book_chapter</type><title>A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity</title><source>Springer Books</source><creator>Brüning, E.</creator><contributor>Blanchard, Philippe ; Dias, Joao-Paulo ; Stubbe, Joachim</contributor><creatorcontrib>Brüning, E. ; Blanchard, Philippe ; Dias, Joao-Paulo ; Stubbe, Joachim</creatorcontrib><description>We prove the existence of solutions u for some semilinear elliptic vector-field equations on IR2 with a nonlinearity which is allowed to grow at infinity ‘nearly like a linear exponential’ in lul. In some cases a growth like exp(alulγ), a > 0 , 0 < γ < 2 , is allowed.
This is achieved by introducing an appropriate space E of ‘à priori-solutions’ for which some important continuous imbeddings are proven replacing the well known Sobolev-imbeddings for the d ≥ 3-dimensional case. Then the standard variational method is applied.</description><identifier>ISSN: 0075-8450</identifier><identifier>ISBN: 9783540519775</identifier><identifier>ISBN: 3540519777</identifier><identifier>EISSN: 1616-6361</identifier><identifier>EISBN: 9783540468684</identifier><identifier>EISBN: 3540468684</identifier><identifier>DOI: 10.1007/BFb0025760</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Russian Mathematical Survey ; Sobolev Imbeddings ; Sobolev Space ; Standard Variational Method ; Symmetric Rearrangement</subject><ispartof>New Methods and Results in Non-linear Field Equations, 2005, p.37-57</ispartof><rights>Springer-Verlag 1989</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Physics</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/BFb0025760$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/BFb0025760$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>775,776,780,789,27902,38232,41418,42487</link.rule.ids></links><search><contributor>Blanchard, Philippe</contributor><contributor>Dias, Joao-Paulo</contributor><contributor>Stubbe, Joachim</contributor><creatorcontrib>Brüning, E.</creatorcontrib><title>A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity</title><title>New Methods and Results in Non-linear Field Equations</title><description>We prove the existence of solutions u for some semilinear elliptic vector-field equations on IR2 with a nonlinearity which is allowed to grow at infinity ‘nearly like a linear exponential’ in lul. In some cases a growth like exp(alulγ), a > 0 , 0 < γ < 2 , is allowed.
This is achieved by introducing an appropriate space E of ‘à priori-solutions’ for which some important continuous imbeddings are proven replacing the well known Sobolev-imbeddings for the d ≥ 3-dimensional case. Then the standard variational method is applied.</description><subject>Russian Mathematical Survey</subject><subject>Sobolev Imbeddings</subject><subject>Sobolev Space</subject><subject>Standard Variational Method</subject><subject>Symmetric Rearrangement</subject><issn>0075-8450</issn><issn>1616-6361</issn><isbn>9783540519775</isbn><isbn>3540519777</isbn><isbn>9783540468684</isbn><isbn>3540468684</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2005</creationdate><recordtype>book_chapter</recordtype><sourceid/><recordid>eNqVj71OAzEQhM2fxAXS8ARb0pjYnH8uJSAiHoD-dEn2wgbHG2yHiLfnoiCoqUaamW-kEeJGqzutlJ88zuZK3Vvv1IkYT31TW6OMa1xjTkWlnXbS1U6f_WZWT72356IaYCsbY9WlGOW8PowYoyuxfoDIBYEjZA67QhwzcA9lz3JJG4x5cLoAGTcUKGKXAEOgbaEFfOKicJI9YVgCfuy6I72n8ga5JI6rYTseKSpf1-Ki70LG8Y9eidvZ8-vTi8zbRHGFqZ0zv-dWq_bwtf37Wv-j-g2lHFZC</recordid><startdate>20050611</startdate><enddate>20050611</enddate><creator>Brüning, E.</creator><general>Springer Berlin Heidelberg</general><scope/></search><sort><creationdate>20050611</creationdate><title>A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity</title><author>Brüning, E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-springer_books_10_1007_BFb00257603</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Russian Mathematical Survey</topic><topic>Sobolev Imbeddings</topic><topic>Sobolev Space</topic><topic>Standard Variational Method</topic><topic>Symmetric Rearrangement</topic><toplevel>online_resources</toplevel><creatorcontrib>Brüning, E.</creatorcontrib></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Brüning, E.</au><au>Blanchard, Philippe</au><au>Dias, Joao-Paulo</au><au>Stubbe, Joachim</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity</atitle><btitle>New Methods and Results in Non-linear Field Equations</btitle><seriestitle>Lecture Notes in Physics</seriestitle><date>2005-06-11</date><risdate>2005</risdate><spage>37</spage><epage>57</epage><pages>37-57</pages><issn>0075-8450</issn><eissn>1616-6361</eissn><isbn>9783540519775</isbn><isbn>3540519777</isbn><eisbn>9783540468684</eisbn><eisbn>3540468684</eisbn><abstract>We prove the existence of solutions u for some semilinear elliptic vector-field equations on IR2 with a nonlinearity which is allowed to grow at infinity ‘nearly like a linear exponential’ in lul. In some cases a growth like exp(alulγ), a > 0 , 0 < γ < 2 , is allowed.
This is achieved by introducing an appropriate space E of ‘à priori-solutions’ for which some important continuous imbeddings are proven replacing the well known Sobolev-imbeddings for the d ≥ 3-dimensional case. Then the standard variational method is applied.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/BFb0025760</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0075-8450 |
| ispartof | New Methods and Results in Non-linear Field Equations, 2005, p.37-57 |
| issn | 0075-8450 1616-6361 |
| language | eng |
| recordid | cdi_springer_books_10_1007_BFb0025760 |
| source | Springer Books |
| subjects | Russian Mathematical Survey Sobolev Imbeddings Sobolev Space Standard Variational Method Symmetric Rearrangement |
| title | A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T13%3A56%3A56IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-springer&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=bookitem&rft.atitle=A%20note%20on%20solutions%20of%20two-dimensional%20semilinear%20elliptic%20vector-field%20equations%20with%20strong%20nonlinearity&rft.btitle=New%20Methods%20and%20Results%20in%20Non-linear%20Field%20Equations&rft.au=Br%C3%BCning,%20E.&rft.date=2005-06-11&rft.spage=37&rft.epage=57&rft.pages=37-57&rft.issn=0075-8450&rft.eissn=1616-6361&rft.isbn=9783540519775&rft.isbn_list=3540519777&rft_id=info:doi/10.1007/BFb0025760&rft_dat=%3Cspringer%3Espringer_books_10_1007_BFb0025760%3C/springer%3E%3Curl%3E%3C/url%3E&rft.eisbn=9783540468684&rft.eisbn_list=3540468684&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |