Singularly perturbed methods for nonlinear elliptic problems:
This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly i...
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| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
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| Schriftenreihe: | Cambridge studies in advanced mathematics
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two relatively simple but typical non-compact elliptic problems. Each chapter then progresses to other related problems to help the reader learn more about the general theories developed from singularly perturbed methods. Designed for PhD students and junior mathematicians intending to do their research in the area of elliptic differential equations, the text covers three main topics. The first is the compactness of the minimization sequences, or the Palais-Smale sequences, or a sequence of approximate solutions; the second is the construction of peak or bubbling solutions by using the Lyapunov-Schmidt reduction method; and the third is the local uniqueness of these solutions |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 29 Jan 2021) |
| Beschreibung: | 1 Online-Ressource (ix, 252 Seiten) |
| ISBN: | 9781108872638 |
| DOI: | 10.1017/9781108872638 |
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| 520 | |a This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two relatively simple but typical non-compact elliptic problems. Each chapter then progresses to other related problems to help the reader learn more about the general theories developed from singularly perturbed methods. Designed for PhD students and junior mathematicians intending to do their research in the area of elliptic differential equations, the text covers three main topics. The first is the compactness of the minimization sequences, or the Palais-Smale sequences, or a sequence of approximate solutions; the second is the construction of peak or bubbling solutions by using the Lyapunov-Schmidt reduction method; and the third is the local uniqueness of these solutions | ||
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| author | Cao, Daomin 1963- Peng, Shuangjie 1968- Yan, Shusen 1963- |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781108872638 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:45:18Z |
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| institution | BVB |
| isbn | 9781108872638 |
| language | English |
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| spelling | Cao, Daomin 1963- (DE-588)1228299323 aut Singularly perturbed methods for nonlinear elliptic problems Daomin Cao, Shuangjie Peng, Shusen Yan Cambridge Cambridge University Press 2021 1 Online-Ressource (ix, 252 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics Title from publisher's bibliographic system (viewed on 29 Jan 2021) This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two relatively simple but typical non-compact elliptic problems. Each chapter then progresses to other related problems to help the reader learn more about the general theories developed from singularly perturbed methods. Designed for PhD students and junior mathematicians intending to do their research in the area of elliptic differential equations, the text covers three main topics. The first is the compactness of the minimization sequences, or the Palais-Smale sequences, or a sequence of approximate solutions; the second is the construction of peak or bubbling solutions by using the Lyapunov-Schmidt reduction method; and the third is the local uniqueness of these solutions Differential equations, Elliptic Differential equations, Nonlinear Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s DE-604 Peng, Shuangjie 1968- (DE-588)1228299560 aut Yan, Shusen 1963- (DE-588)1228299757 aut Erscheint auch als Druck-Ausgabe 978-1-108-83683-8 https://doi.org/10.1017/9781108872638 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Cao, Daomin 1963- Peng, Shuangjie 1968- Yan, Shusen 1963- Singularly perturbed methods for nonlinear elliptic problems Differential equations, Elliptic Differential equations, Nonlinear Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| subject_GND | (DE-588)4310554-3 |
| title | Singularly perturbed methods for nonlinear elliptic problems |
| title_auth | Singularly perturbed methods for nonlinear elliptic problems |
| title_exact_search | Singularly perturbed methods for nonlinear elliptic problems |
| title_exact_search_txtP | Singularly perturbed methods for nonlinear elliptic problems |
| title_full | Singularly perturbed methods for nonlinear elliptic problems Daomin Cao, Shuangjie Peng, Shusen Yan |
| title_fullStr | Singularly perturbed methods for nonlinear elliptic problems Daomin Cao, Shuangjie Peng, Shusen Yan |
| title_full_unstemmed | Singularly perturbed methods for nonlinear elliptic problems Daomin Cao, Shuangjie Peng, Shusen Yan |
| title_short | Singularly perturbed methods for nonlinear elliptic problems |
| title_sort | singularly perturbed methods for nonlinear elliptic problems |
| topic | Differential equations, Elliptic Differential equations, Nonlinear Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| topic_facet | Differential equations, Elliptic Differential equations, Nonlinear Nichtlineare elliptische Differentialgleichung |
| url | https://doi.org/10.1017/9781108872638 |
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