Topological Degree Approach to Bifurcation Problems (Paperback, Softcover reprint of hardcover 1st ed. 2008)

1. 1 Preface Many phenomena from physics, biology, chemistry and economics are modeled by di?erential equations with parameters. When a nonlinear equation is est- lished, its behavior/dynamics should be understood. In general, it is impossible to ?nd a complete dynamics of a nonlinear di?erential equation. Hence at least, either periodic or irregular/chaotic solutions are tried to be shown. So a pr- erty of a desired solution of a nonlinear equation is given as a parameterized boundary value problem. Consequently, the task is transformed to a solvability of an abstract nonlinear equation with parameters on a certain functional space. When a family of solutions of the abstract equation is known for some para- ters, the persistence or bifurcations of solutions from that family is studied as parameters are changing. There are several approaches to handle such nonl- ear bifurcation problems. One of them is a topological degree method, which is rather powerful in cases when nonlinearities are not enough smooth. The aim of this book is to present several original bifurcation results achieved by the author using the topological degree theory. The scope of the results is rather broad from showing periodic and chaotic behavior of non-smooth mechanical systems through the existence of traveling waves for ordinary di?erential eq- tions on in?nite lattices up to study periodic oscillations of undamped abstract waveequationsonHilbertspaceswithapplicationstononlinearbeamandstring partial di?erential equations. 1.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Topological Fixed Point Theory and Its Applications, 5
Release date:	November 2010
First published:	2008
Authors:	Michal Feckan
Dimensions:	235 x 155 x 14mm (L x W x T)
Format:	Paperback
Pages:	261
Edition:	Softcover reprint of hardcover 1st ed. 2008
ISBN-13:	978-90-481-7969-5
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis Books > Science & Mathematics > Mathematics > Topology > General Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science Books > Science & Mathematics > Physics > Classical mechanics > General Books > Professional & Technical > Mechanical engineering & materials > Materials science > Mechanics of solids > Dynamics & vibration
LSN:	90-481-7969-6
Barcode:	9789048179695

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