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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Brouwer Degree - The Core of Nonlinear Analysis (Hardcover, 1st ed. 2021)
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Brouwer Degree - The Core of Nonlinear Analysis (Hardcover, 1st ed. 2021)
Series: Progress in Nonlinear Differential Equations and Their Applications, 95
Expected to ship within 10 - 15 working days
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This monograph explores the concept of the Brouwer degree and its
continuing impact on the development of important areas of
nonlinear analysis. The authors define the degree using an
analytical approach proposed by Heinz in 1959 and further developed
by Mawhin in 2004, linking it to the Kronecker index and employing
the language of differential forms. The chapters are organized so
that they can be approached in various ways depending on the
interests of the reader. Unifying this structure is the central
role the Brouwer degree plays in nonlinear analysis, which is
illustrated with existence, surjectivity, and fixed point theorems
for nonlinear mappings. Special attention is paid to the
computation of the degree, as well as to the wide array of
applications, such as linking, differential and partial
differential equations, difference equations, variational and
hemivariational inequalities, game theory, and mechanics. Each
chapter features bibliographic and historical notes, and the final
chapter examines the full history. Brouwer Degree will serve as an
authoritative reference on the topic and will be of interest to
professional mathematicians, researchers, and graduate students.
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