Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2002
|
| Series: | Mathematics and Its Applications
550 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Preface Constructing nonlinear parameter-dependent mathematical models is essential in modeling in many scientific research fields. The investigation of branching (bifurcating) solutions of such equations is one of the most important aspects in the analysis of such models. The foundations of the theory of bifurcations for the functional equations were laid in the well known publications by AM. Lyapunov (1906) [1, vol. 4] (on equilibrium forms of rotating liquids) and E. Schmidt (1908) [1]. The approach proposed by them has been throughly developed and is presently known as the Lyapunov-Schmidt method (see M.M. Vainberg and V.A Trenogin [1, 2]). A valuable part in the foundations of the bifurcation theory belongs to A. Poincares ideas [1]. Later, to the end of proving the theorems on existence of bifurcation points, infinite-dimensional generalizations of topological and variational methods were proposed by M.A Krasnoselsky [1], M.M. Vainberg [1] and others. A great contribution to the development and applications of the bifurcation theory has been made by a number of famous 20th century pure and applied mathematicians (for example, see the bibliography in E. Zeidler [1]) |
| Physical Description: | 1 Online-Ressource (XX, 548 p) |
| ISBN: | 9789401721226 9789048161508 |
| DOI: | 10.1007/978-94-017-2122-6 |
Staff View
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| 490 | 1 | |a Mathematics and Its Applications |v 550 | |
| 500 | |a Preface Constructing nonlinear parameter-dependent mathematical models is essential in modeling in many scientific research fields. The investigation of branching (bifurcating) solutions of such equations is one of the most important aspects in the analysis of such models. The foundations of the theory of bifurcations for the functional equations were laid in the well known publications by AM. Lyapunov (1906) [1, vol. 4] (on equilibrium forms of rotating liquids) and E. Schmidt (1908) [1]. The approach proposed by them has been throughly developed and is presently known as the Lyapunov-Schmidt method (see M.M. Vainberg and V.A Trenogin [1, 2]). A valuable part in the foundations of the bifurcation theory belongs to A. Poincares ideas [1]. Later, to the end of proving the theorems on existence of bifurcation points, infinite-dimensional generalizations of topological and variational methods were proposed by M.A Krasnoselsky [1], M.M. Vainberg [1] and others. A great contribution to the development and applications of the bifurcation theory has been made by a number of famous 20th century pure and applied mathematicians (for example, see the bibliography in E. Zeidler [1]) | ||
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| 700 | 1 | |a Sinitsyn, Aleksandr |e Sonstige |4 oth | |
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| id | DE-604.BV042424280 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401721226 9789048161508 |
| language | English |
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| series2 | Mathematics and Its Applications |
| spelling | Sidorov, Nikolay Verfasser aut Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications by Nikolay Sidorov, Boris Loginov, Aleksandr Sinitsyn, Michail Falaleev Dordrecht Springer Netherlands 2002 1 Online-Ressource (XX, 548 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 550 Preface Constructing nonlinear parameter-dependent mathematical models is essential in modeling in many scientific research fields. The investigation of branching (bifurcating) solutions of such equations is one of the most important aspects in the analysis of such models. The foundations of the theory of bifurcations for the functional equations were laid in the well known publications by AM. Lyapunov (1906) [1, vol. 4] (on equilibrium forms of rotating liquids) and E. Schmidt (1908) [1]. The approach proposed by them has been throughly developed and is presently known as the Lyapunov-Schmidt method (see M.M. Vainberg and V.A Trenogin [1, 2]). A valuable part in the foundations of the bifurcation theory belongs to A. Poincares ideas [1]. Later, to the end of proving the theorems on existence of bifurcation points, infinite-dimensional generalizations of topological and variational methods were proposed by M.A Krasnoselsky [1], M.M. Vainberg [1] and others. A great contribution to the development and applications of the bifurcation theory has been made by a number of famous 20th century pure and applied mathematicians (for example, see the bibliography in E. Zeidler [1]) Mathematics Functional analysis Differential equations, partial Algorithms Partial Differential Equations Functional Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mathematik Loginov, Boris Sonstige oth Sinitsyn, Aleksandr Sonstige oth Falaleev, Michail Sonstige oth Mathematics and Its Applications 550 (DE-604)BV008163334 550 https://doi.org/10.1007/978-94-017-2122-6 Verlag Volltext |
| spellingShingle | Sidorov, Nikolay Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications Mathematics and Its Applications Mathematics Functional analysis Differential equations, partial Algorithms Partial Differential Equations Functional Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mathematik |
| title | Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications |
| title_auth | Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications |
| title_exact_search | Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications |
| title_full | Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications by Nikolay Sidorov, Boris Loginov, Aleksandr Sinitsyn, Michail Falaleev |
| title_fullStr | Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications by Nikolay Sidorov, Boris Loginov, Aleksandr Sinitsyn, Michail Falaleev |
| title_full_unstemmed | Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications by Nikolay Sidorov, Boris Loginov, Aleksandr Sinitsyn, Michail Falaleev |
| title_short | Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications |
| title_sort | lyapunov schmidt methods in nonlinear analysis and applications |
| topic | Mathematics Functional analysis Differential equations, partial Algorithms Partial Differential Equations Functional Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mathematik |
| topic_facet | Mathematics Functional analysis Differential equations, partial Algorithms Partial Differential Equations Functional Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Mathematik |
| url | https://doi.org/10.1007/978-94-017-2122-6 |
| volume_link | (DE-604)BV008163334 |
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