Titlebook: Bifurcation Theory; An Introduction with Hansj?rg Kielh?fer Textbook 20041st edition Springer-Verlag New York 2004 Vibration.bifurcation.bi

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Local Theory,One of the most important analytic tools for the solution of a nonlinear problem,.where . is a mapping .: . × . → . with open sets . ? ., . ? ., and where . are (real) Banach spaces, is the following .:

ULCER

Introduction,ing of the Euler rod, the appearance of Taylor vortices, and the onset of oscillations in an electric circuit, for instance, all have a common cause: A specific physical parameter crosses a threshold, and that event forces the system to the organization of a new state that differs considerably from

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Applications,that property, but we have infinite-dimensional applications in mind. A prototype of a Fredholm operator, playing also a central role in applications, is an elliptic operator over a bounded domain. We confine ourselves to operators of second order acting on scalar functions.

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0066-5452 ed presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory t

CRUDE

Karl Farmer,Birgit Bednar-Friedlus mapping is accomplished by approximation. (The procedure expounded in Section II.5 for proper Fredholm operators applies in a simplified form for the finite-dimensional case of this section, too, yielding proofs for all statements.)

Expostulate

Textbook 20041st editionation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems

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Textbook 20041st editionions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.