Critical Point Theory and Hamiltonian Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1989
|
| Schriftenreihe: | Applied Mathematical Sciences
74 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN |
| Beschreibung: | 1 Online-Ressource (XIV, 278 p) |
| ISBN: | 9781475720617 9781441930897 |
| DOI: | 10.1007/978-1-4757-2061-7 |
Internformat
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| 500 | |a FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN | ||
| 650 | 4 | |a Physics | |
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Datensatz im Suchindex
| _version_ | 1804153094210060288 |
|---|---|
| any_adam_object | |
| author | Mawhin, Jean L. 1942- |
| author_GND | (DE-588)135657210 |
| author_facet | Mawhin, Jean L. 1942- |
| author_role | aut |
| author_sort | Mawhin, Jean L. 1942- |
| author_variant | j l m jl jlm |
| building | Verbundindex |
| bvnumber | BV042421307 |
| classification_tum | MAT 000 |
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| dewey-full | 530.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 530.1 |
| dewey-search | 530.1 |
| dewey-sort | 3530.1 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-1-4757-2061-7 |
| format | Electronic eBook |
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| id | DE-604.BV042421307 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781475720617 9781441930897 |
| language | English |
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| oclc_num | 864055060 |
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| physical | 1 Online-Ressource (XIV, 278 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Springer New York |
| record_format | marc |
| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | Mawhin, Jean L. 1942- Verfasser (DE-588)135657210 aut Critical Point Theory and Hamiltonian Systems by Jean Mawhin, Michel Willem New York, NY Springer New York 1989 1 Online-Ressource (XIV, 278 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 74 FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN Physics Theoretical, Mathematical and Computational Physics Kritischer Punkt (DE-588)4140476-2 gnd rswk-swf Kritischer Punkt Mathematik (DE-588)4207169-0 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Kritischer Punkt Mathematik (DE-588)4207169-0 s 1\p DE-604 Kritischer Punkt (DE-588)4140476-2 s 2\p DE-604 Willem, Michel Sonstige oth Applied Mathematical Sciences 74 (DE-604)BV040244599 74 https://doi.org/10.1007/978-1-4757-2061-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mawhin, Jean L. 1942- Critical Point Theory and Hamiltonian Systems Applied Mathematical Sciences Physics Theoretical, Mathematical and Computational Physics Kritischer Punkt (DE-588)4140476-2 gnd Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4140476-2 (DE-588)4207169-0 (DE-588)4139943-2 |
| title | Critical Point Theory and Hamiltonian Systems |
| title_auth | Critical Point Theory and Hamiltonian Systems |
| title_exact_search | Critical Point Theory and Hamiltonian Systems |
| title_full | Critical Point Theory and Hamiltonian Systems by Jean Mawhin, Michel Willem |
| title_fullStr | Critical Point Theory and Hamiltonian Systems by Jean Mawhin, Michel Willem |
| title_full_unstemmed | Critical Point Theory and Hamiltonian Systems by Jean Mawhin, Michel Willem |
| title_short | Critical Point Theory and Hamiltonian Systems |
| title_sort | critical point theory and hamiltonian systems |
| topic | Physics Theoretical, Mathematical and Computational Physics Kritischer Punkt (DE-588)4140476-2 gnd Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Physics Theoretical, Mathematical and Computational Physics Kritischer Punkt Kritischer Punkt Mathematik Hamiltonsches System |
| url | https://doi.org/10.1007/978-1-4757-2061-7 |
| volume_link | (DE-604)BV040244599 |
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