ISBN: 9781402087240

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/dyn… More...

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. Topological Degree Approach to Bifurcation Problems: 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. Boundary value problem Topology Vibration calculus differential topology friction partial differential equation wave equation C Analysis Dynamical Systems and Ergodic Theory Topology Mechanics Vibration, Dynamical Systems, Control Mathematic, Springer Netherland<

ISBN: 9781402087240

This book contains original bifurcation results for the existence of oscillations and chaotic behavior of differential equations and discrete dynamical systems under variation of involved… More...

This book contains original bifurcation results for the existence of oscillations and chaotic behavior of differential equations and discrete dynamical systems under variation of involved parameters. It studies a broad variety of nonlinear problems.; EPUB; Scientific, Technical and Medical > Mathematics > Topology, Random House<

2008, ISBN: 9781402087240

eBooks, eBook Download (PDF), 2008, [PU: Springer Netherland], Springer Netherland, 2008

2009, ISBN: 9781402087240

[ED: 2008], eBook Download (PDF), eBooks, [PU: Springer Netherland]

2008, ISBN: 9781402087240

[ED: 1], Auflage, eBook Download (PDF), eBooks, [PU: Springer-Verlag]