Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications

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]).

List of contents

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 Convex Majorants in Nonlinear Analysis.- 5. Methods of Representation Theory and Group Analysis in Bifurcation Theory.- 6. Singular Dih'ferential 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.

Product details

• Authors: M. V. Falaleev, M.V. Falaleev, Bori Loginov, Boris Loginov, Nikola Sidorov, Nikolay Sidorov, A V et a Sinitsyn, A. V. Sinitsyn, A.V. Sinitsyn, Aleksandr Sinitsyn
• Publisher: Springer Netherlands
• Languages: English
• Product format: Paperback / Softback
• Released: 08.10.2010
• EAN: 9789048161508
• ISBN: 978-90-481-6150-8
• No. of pages: 548
• Illustrations: XX, 548 p.
• Series: Mathematics and Its Applications; Mathematics and Its Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; C, Algorithms, Mathematics and Statistics, Applications of Mathematics, Functional Analysis, Numerical analysis, Partial Differential Equations, Differential equations, Engineering mathematics, Applied mathematics, Maths for engineers, Mathematical modelling, Mathematical Modeling and Industrial Mathematics, Mathematical models, Functional analysis & transforms