dc.contributor.advisor Hill, C. K. dc.creator Pillay, Paranjothi. dc.date.accessioned 2013-10-21T11:07:23Z dc.date.available 2013-10-21T11:07:23Z dc.date.created 1989 dc.date.issued 2013-10-21 dc.identifier.uri http://hdl.handle.net/10413/9795 dc.description Thesis (M.Sc.)-University of Durban-Westville, 1989. en dc.description.abstract The objective of this dissertation is to expand on the proofs and concepts of Degree Theory, dealt with in chapters 1 and 2 of Deimling , to make it more readable and en accessible to anyone who is interested in the field. Chapter 1 is an introduction and contains the basic requirements for the subsequent chapters. The remaining chapters aim at defining a ll-valued map D (the degree) on the set M = {(F, Ω, y) / Ω C X open, F : Ὠ → X, y ɇ F(∂Ω)} (each time, the elements of M satisfying extra conditions) that satisfies : (D1) D(I, Ω, y) = 1 if y Є Ω. (D2) D(F, Ω, y) = D(F, Ω1 , y) + D(F, Ω2, y) if Ω1 and Ω2 are disjoint open subsets of Ω o such that y ɇ F(Ὠ \ Ω1 U Ω2 ). (D3) D(I - H(t, .), Ω, y(t)) is independent of t if H : J x Ὠ →X and y : J → X. An important property that follows from these three properties is (D4) F-1(y) ≠ Ø if D(F, Ω, y) ≠ 0. This property ensures that equations of the form Fx = y have solutions if D(F, Ω, y) ≠ 0. Another property that features in these chapters is the Borsuk property which gives us conditions under which the degree is odd and hence nonzero. dc.language.iso en_ZA en dc.subject Nonlinear functional analysis. en dc.subject Theses--Mathematics. en dc.title Degree theory in nonlinear functional analysis. en dc.type Thesis en
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