Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications

Nikolay Sidorov

ISBN 10: 1402009410 / ISBN 13: 9781402009419

Edité par Springer-Verlag New York Inc., 2002

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This item is printed on demand. New copy - Usually dispatched within 5-9 working days 1003.

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Détails bibliographiques

• Titre: Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications
• Éditeur: Springer-Verlag New York Inc.
• Date de parution: 2002
• Langue: anglais
• ISBN à 10 chiffres: 1402009410
• ISBN à 13 chiffres: 9781402009419
• Reliure: Hardback
• État de l'article: New
• Poids: 1003 grammes

A propos de ce titre

Synopsis

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]).

Présentation de l'éditeur

This book concentrates on the branching solutions of nonlinear operator equations and the theory of degenerate operator-differential equations especially applicable to algorithmic analysis and nonlinear PDE's in mechanics and mathematical physics. The authors expound the recent result on the generalized eigen-value problem, the perturbation method, Schmidt's pseudo-inversion for regularization of linear and nonlinear problems in the branching theory and group methods in bifurcation theory. The book covers regular iterative methods in a neighborhood of branch points and the theory of differential-operator equations with a non-invertible operator in the main expression is constructed. Various recent results on theorems of existence are given including asymptotic, approximate and group methods.