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024 7 $a10.1007/978-3-030-63230-4
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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aBrouwer degree $ethe core of nonlinear analysis /$fGeorge Dinca and Jean Mawhin
205   $a1st ed. 2021.
210  1$aCham, Switzerland :$cSpringer,$d[2021]
210  4$d©2021
215   $a1 online resource (XIX, 447 p. 2 illus. in color.)
225 1 $aProgress in Nonlinear Differential Equations and Their Applications,$x1421-1750 ;$v95
320   $aIncludes bibliographical references and index.
327   $aThe 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.
330   $aThis monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.
410  0$aProgress in nonlinear differential equations and their applications$x1421-1750 ;$v95.
606   $aNonlinear functional analysis
606   $aNonlinear analysis
606   $aAnàlisi funcional no lineal$2thub
608   $aLlibres electrònics$2thub
615  0$aNonlinear functional analysis.
615  0$aNonlinear analysis.
615  7$aAnàlisi funcional no lineal
676   $a515.7
700   $aDinca?$b Gheorghe$01074838
702   $aMawhin$b J.
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910484940803321
996   $aBrouwer degree$92582621
997   $aUNINA