Degree Theory

Dumitru Motreanu, Viorica Venera Motreanu and Nikolaos Papageorgiou
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Dumitru Motreanu: University of Perpignan, Department of Mathematics
Viorica Venera Motreanu: Ben-Gurion University of the Negev, Department of Mathematics
Nikolaos Papageorgiou: National Technical University, Department of Mathematics

Chapter Chapter 4 in Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 2014, pp 61-96 from Springer

Abstract: Abstract This chapter provides the fundamental elements of degree theory used later in the book for showing abstract results of critical point theory or bifurcation theory as well as for the study of the existence and multiplicity of solutions to nonlinear problems. The first section of the chapter introduces Brouwer’s degree and its important applications such as Brouwer’s fixed point theorem, Borsuk’s theorem, Borsuk–Ulam, and Lyusternik–Schnirelmann–Borsuk theorems. The second section sets forth the Leray–Schauder degree theory for compact perturbations of the identity. The third section amounts to a description of the degree for (S)+maps using Galerkin approximations and construction of the degree theory for multifunctions of the form f + A with f an (S)+-map and A a maximal monotone operator. Comments and historical notes are given in a remarks section.

Keywords: Degree Theory; Leray-Schauder Degree; Compact Perturbation; Galerkin Approximation; Borsuk (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-9323-5_4

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DOI: 10.1007/978-1-4614-9323-5_4

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