Geometrical Methods of Nonlinear Analysis: 263 (Grundlehren der mathematischen Wissenschaften, 263) - Softcover

Krasnoselskii, M. A.; Zabreiko, P. P.

Softcover

ISBN 10: 364269411X ISBN 13: 9783642694110

Publisher: Springer, 2011

Synopsis

Geometrical (in particular, topological) methods in nonlinear analysis were originally invented by Banach, Birkhoff, Kellogg, Schauder, Leray, and others in existence proofs. Since about the fifties, these methods turned out to be essentially the sole approach to a variety of new problems: the investigation of iteration processes and other procedures in numerical analysis, in bifur­ cation problems and branching of solutions, estimates on the number of solutions and criteria for the existence of nonzero solutions, the analysis of the structure of the solution set, etc. These methods have been widely applied to the theory of forced vibrations and auto-oscillations, to various problems in the theory of elasticity and fluid. mechanics, to control theory, theoretical physics, and various parts of mathematics. At present, nonlinear analysis along with its geometrical, topological, analytical, variational, and other methods is developing tremendously thanks to research work in many countries. Totally new ideas have been advanced, difficult problems have been solved, and new applications have been indicated. To enumerate the publications of the last few years one would need dozens of pages. On the other hand, many problems of non­ linear analysis are still far from a solution (problems arising from the internal development of mathematics and, in particular, problems arising in the process of interpreting new problems in the natural sciences). We hope that the English edition of our book will contribute to the further propagation of the ideas of nonlinear analysis.

Edition details

• Publisher: Springer
• Publication date: 2011
• Language: English
• ISBN 10: 364269411X
• ISBN 13: 9783642694110
• Binding: Paperback
• Number of pages: 432