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Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications (Hardcover, 2002 ed.)
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Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications (Hardcover, 2002 ed.)
Series: Mathematics and Its Applications, 550
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Total price: R3,326
Discovery Miles: 33 260
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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]).
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