Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications

Nikolay Sidorov

ISBN 10: 1402009410 / ISBN 13: 9781402009419

Verlag: Springer Netherlands, Springer Netherlands, 2002

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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]).

Bestandsnummer des Verkäufers 9781402009419

Bibliografische Details

• Titel: Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications
• Verlag: Springer Netherlands, Springer Netherlands
• Erscheinungsjahr: 2002
• Sprache: Englisch
• ISBN-10: 1402009410
• ISBN-13: 9781402009419
• Einband: Buch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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]).