Brouwer degree : the core of nonlinear analysis / George Dinca and Jean Mawhin.

Format:

Book

Author/Creator:

Dincă, George, author.

Mawhin, J., author.

Series:

Progress in nonlinear differential equations and their applications 1421-1750 ; 95.

Progress in Nonlinear Differential Equations and Their Applications, 1421-1750 ; 95

Language:

English

Subjects (All):

Nonlinear functional analysis.

Nonlinear analysis.

Physical Description:

1 online resource (XIX, 447 p. 2 illus. in color.)

Edition:

1st ed. 2021.

Place of Publication:

Cham, Switzerland : Springer, [2021]

System Details:

Mode of access: World Wide Web.

Summary:

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.

Contents:

The Kronecker Index and the Brouwer Degree

Continuation, Existence, and Bifurcation

Infinite-Dimensional Problems

Difference Equations

Periodic Solutions of Differential Systems

Two-Dimensional Problems

The Degree of Some Classes of Mappings

History of Brouwer Fixed Point Theorem.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

3-030-63230-X