Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications: 550 - Rilegato

Loginov, Boris; Sinitsyn, Aleksandr; Falaleev, Michail

 
9781402009419: Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications: 550
Rilegato
ISBN 10: 1402009410 ISBN 13: 9781402009419
Casa editrice: Kluwer Academic Pub, 2002

Sinossi

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 bifurca­ tions for the functional equations were laid in the well known publications by AM. Lyapunov (1906) [1, vol. 4] (on equilibrium forms of rotating liq­ uids) 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 founda­ tions 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 mathe­ maticians (for example, see the bibliography in E. Zeidler [1]).

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Contenuti

Preface. 1. On Regularization of Linear Equations on the Basis of Perturbation Theory. 2. Investigation of Bifurcation Points of a Nonlinear Equations. 3. Regularization of Computation of Solutions in a Neighborhood of the Branch Point. 4. Iterations, Interlaced Equations and Lyapunov Conbex Majorants in Nonlinear Analysis. 5. Methods of Representation Theory and Group Analysis in Bifurcation Theory. 6. Singular Differential Equations in Banach Spaces. 7. Steady-State Solutions of the Vlasov-Maxwell System. Appendices. A: Positive solutions of the nonlinear singular boundary value problem of magnetic insulation. References. Index.

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Editore
Kluwer Academic Pub
Data di pubblicazione
2002
Lingua
Inglese
ISBN 10 
1402009410
ISBN 13 
9781402009419
Rilegatura
Copertina rigida
Numero di pagine
566
Redattore
Sidorov Nikolay
Contatto del produttore
non disponibile
Persona responsabile
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Altre edizioni note dello stesso titolo

9789048161508: Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications: 550

Edizione in evidenza

ISBN 10:  9048161509 ISBN 13:  9789048161508
Casa editrice: Springer, 2010
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