Methods of Bifurcation Theory:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
New York, NY
Springer New York
1982
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Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
251 |
Schlagworte: | |
Online-Zugang: | Volltext |
Beschreibung: | An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable |
Beschreibung: | 1 Online-Ressource (XV, 525p. 97 illus) |
ISBN: | 9781461381594 9781461381617 |
ISSN: | 0072-7830 |
DOI: | 10.1007/978-1-4613-8159-4 |
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Datensatz im Suchindex
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---|---|
any_adam_object | |
author | Chow, Shui-Nee |
author_facet | Chow, Shui-Nee |
author_role | aut |
author_sort | Chow, Shui-Nee |
author_variant | s n c snc |
building | Verbundindex |
bvnumber | BV042420674 |
classification_tum | MAT 000 |
collection | ZDB-2-SMA ZDB-2-BAE |
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dewey-full | 515 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515 |
dewey-search | 515 |
dewey-sort | 3515 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
doi_str_mv | 10.1007/978-1-4613-8159-4 |
format | Electronic eBook |
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institution | BVB |
isbn | 9781461381594 9781461381617 |
issn | 0072-7830 |
language | English |
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physical | 1 Online-Ressource (XV, 525p. 97 illus) |
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spelling | Chow, Shui-Nee Verfasser aut Methods of Bifurcation Theory by Shui-Nee Chow, Jack K. Hale New York, NY Springer New York 1982 1 Online-Ressource (XV, 525p. 97 illus) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 251 0072-7830 An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable Mathematics Global analysis (Mathematics) Analysis Mathematik Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Funktional-Differentialgleichung (DE-588)4155668-9 gnd rswk-swf Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Verzweigung Mathematik (DE-588)4078889-1 s Nichtlineare Funktionalanalysis (DE-588)4042093-0 s 1\p DE-604 Nichtlineare Differentialgleichung (DE-588)4205536-2 s 2\p DE-604 Mannigfaltigkeit (DE-588)4037379-4 s 3\p DE-604 Funktional-Differentialgleichung (DE-588)4155668-9 s 4\p DE-604 Hale, Jack K. Sonstige oth https://doi.org/10.1007/978-1-4613-8159-4 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Chow, Shui-Nee Methods of Bifurcation Theory Mathematics Global analysis (Mathematics) Analysis Mathematik Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Funktional-Differentialgleichung (DE-588)4155668-9 gnd Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
subject_GND | (DE-588)4205536-2 (DE-588)4155668-9 (DE-588)4042093-0 (DE-588)4078889-1 (DE-588)4012249-9 (DE-588)4037379-4 |
title | Methods of Bifurcation Theory |
title_auth | Methods of Bifurcation Theory |
title_exact_search | Methods of Bifurcation Theory |
title_full | Methods of Bifurcation Theory by Shui-Nee Chow, Jack K. Hale |
title_fullStr | Methods of Bifurcation Theory by Shui-Nee Chow, Jack K. Hale |
title_full_unstemmed | Methods of Bifurcation Theory by Shui-Nee Chow, Jack K. Hale |
title_short | Methods of Bifurcation Theory |
title_sort | methods of bifurcation theory |
topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Funktional-Differentialgleichung (DE-588)4155668-9 gnd Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Nichtlineare Differentialgleichung Funktional-Differentialgleichung Nichtlineare Funktionalanalysis Verzweigung Mathematik Differentialgleichung Mannigfaltigkeit |
url | https://doi.org/10.1007/978-1-4613-8159-4 |
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