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Nonlinearity and Functional Analysis - Lectures on Nonlinear Problems in Mathematical Analysis (Hardcover)
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Nonlinearity and Functional Analysis - Lectures on Nonlinear Problems in Mathematical Analysis (Hardcover)
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Nonlinearity and Functional Analysis is a collection of lectures
that aim to present a systematic description of fundamental
nonlinear results and their applicability to a variety of concrete
problems taken from various fields of mathematical analysis. For
decades, great mathematical interest has focused on problems
associated with linear operators and the extension of the
well-known results of linear algebra to an infinite-dimensional
context. This interest has been crowned with deep insights, and the
substantial theory that has been developed has had a profound
influence throughout the mathematical sciences. This volume
comprises six chapters and begins by presenting some background
material, such as differential-geometric sources, sources in
mathematical physics, and sources from the calculus of variations,
before delving into the subject of nonlinear operators. The
following chapters then discuss local analysis of a single mapping
and parameter dependent perturbation phenomena before going into
analysis in the large. The final chapters conclude the collection
with a discussion of global theories for general nonlinear
operators and critical point theory for gradient mappings. This
book will be of interest to practitioners in the fields of
mathematics and physics, and to those with interest in conventional
linear functional analysis and ordinary and partial differential
equations.
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