Periodic Solutions of Singular Lagrangian Systems:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1993
|
| Schriftenreihe: | Progress in Nonlinear Differential Equations and Their Applications
10 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-1-4612-0319-3 |
| Beschreibung: | This monograph deals with the existence of periodic motions of Lagrangian systems with n degrees of freedom ij + V'(q) =0, where V is a singular potential. A prototype of such a problem, even if it is not the only physically interesting one, is the Kepler problem .. q 0 q+yqr= . This, jointly with the more general N-body problem, has always been the object of a great deal of research. Most of those results are based on perturbation methods, and make use of the specific features of the Kepler potential. Our approach is more on the lines of Nonlinear Functional Analysis: our main purpose is to give a functional frame for systems with singular potentials, including the Kepler and the N-body problem as particular cases. Precisely we use Critical Point Theory to obtain existence results, qualitative in nature, which hold true for broad classes of potentials. This highlights that the variational methods, which have been employed to obtain important advances in the study of regular Hamiltonian systems, can be successfally used to handle singular potentials as well. The research on this topic is still in evolution, and therefore the results we will present are not to be intended as the final ones. Indeed a major purpose of our discussion is to present methods and tools which have been used in studying such problems. Vlll PREFACE Part of the material of this volume has been presented in a series of lectures given by the authors at SISSA, Trieste, whom we would like to thank for their hospitality and support. We wish also to thank Ugo Bessi, Paolo Caldiroli, Fabio Giannoni, Louis Jean jean, Lorenzo Pisani, Enrico Serra, Kazunaka Tanaka, Enzo Vitillaro for helpful suggestions. May 26, 1993 |
| Umfang: | 1 Online-Ressource (XII, 160 p) |
| ISBN: | 9781461203193 9781461267058 |
| DOI: | 10.1007/978-1-4612-0319-3 |
Internformat
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| 490 | 1 | |a Progress in Nonlinear Differential Equations and Their Applications |v 10 | |
| 500 | |a This monograph deals with the existence of periodic motions of Lagrangian systems with n degrees of freedom ij + V'(q) =0, where V is a singular potential. A prototype of such a problem, even if it is not the only physically interesting one, is the Kepler problem .. q 0 q+yqr= . This, jointly with the more general N-body problem, has always been the object of a great deal of research. Most of those results are based on perturbation methods, and make use of the specific features of the Kepler potential. Our approach is more on the lines of Nonlinear Functional Analysis: our main purpose is to give a functional frame for systems with singular potentials, including the Kepler and the N-body problem as particular cases. Precisely we use Critical Point Theory to obtain existence results, qualitative in nature, which hold true for broad classes of potentials. This highlights that the variational methods, which have been employed to obtain important advances in the study of regular Hamiltonian systems, can be successfally used to handle singular potentials as well. | ||
| 500 | |a The research on this topic is still in evolution, and therefore the results we will present are not to be intended as the final ones. Indeed a major purpose of our discussion is to present methods and tools which have been used in studying such problems. Vlll PREFACE Part of the material of this volume has been presented in a series of lectures given by the authors at SISSA, Trieste, whom we would like to thank for their hospitality and support. We wish also to thank Ugo Bessi, Paolo Caldiroli, Fabio Giannoni, Louis Jean jean, Lorenzo Pisani, Enrico Serra, Kazunaka Tanaka, Enzo Vitillaro for helpful suggestions. May 26, 1993 | ||
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| author | Ambrosetti, Antonio 1944-2020 |
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| author_facet | Ambrosetti, Antonio 1944-2020 |
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| building | Verbundindex |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0319-3 |
| format | Electronic eBook |
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| id | DE-604.BV042419501 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:40Z |
| institution | BVB |
| isbn | 9781461203193 9781461267058 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854918 |
| oclc_num | 869872351 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 160 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Birkhäuser Boston |
| record_format | marc |
| series | Progress in Nonlinear Differential Equations and Their Applications |
| series2 | Progress in Nonlinear Differential Equations and Their Applications |
| spellingShingle | Ambrosetti, Antonio 1944-2020 Periodic Solutions of Singular Lagrangian Systems Progress in Nonlinear Differential Equations and Their Applications Mathematics Differential equations, partial Partial Differential Equations Mathematik Periodische Lösung (DE-588)4199269-6 gnd Kritischer Punkt (DE-588)4140476-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4199269-6 (DE-588)4140476-2 (DE-588)4137931-7 |
| title | Periodic Solutions of Singular Lagrangian Systems |
| title_auth | Periodic Solutions of Singular Lagrangian Systems |
| title_exact_search | Periodic Solutions of Singular Lagrangian Systems |
| title_full | Periodic Solutions of Singular Lagrangian Systems by Antonio Ambrosetti, Vittorio Coti Zelati |
| title_fullStr | Periodic Solutions of Singular Lagrangian Systems by Antonio Ambrosetti, Vittorio Coti Zelati |
| title_full_unstemmed | Periodic Solutions of Singular Lagrangian Systems by Antonio Ambrosetti, Vittorio Coti Zelati |
| title_short | Periodic Solutions of Singular Lagrangian Systems |
| title_sort | periodic solutions of singular lagrangian systems |
| topic | Mathematics Differential equations, partial Partial Differential Equations Mathematik Periodische Lösung (DE-588)4199269-6 gnd Kritischer Punkt (DE-588)4140476-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Mathematics Differential equations, partial Partial Differential Equations Mathematik Periodische Lösung Kritischer Punkt Differenzierbares dynamisches System |
| url | https://doi.org/10.1007/978-1-4612-0319-3 |
| volume_link | (DE-604)BV036582883 |
| work_keys_str_mv | AT ambrosettiantonio periodicsolutionsofsingularlagrangiansystems AT cotizelativittorio periodicsolutionsofsingularlagrangiansystems |