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dc.contributor.advisorHill, C. K.
dc.creatorPillay, Paranjothi.
dc.date.accessioned2013-10-21T11:07:23Z
dc.date.available2013-10-21T11:07:23Z
dc.date.created1989
dc.date.issued2013-10-21
dc.identifier.urihttp://hdl.handle.net/10413/9795
dc.descriptionThesis (M.Sc.)-University of Durban-Westville, 1989.en
dc.description.abstractThe objective of this dissertation is to expand on the proofs and concepts of Degree Theory, dealt with in chapters 1 and 2 of Deimling [28], to make it more readable and 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.en
dc.language.isoen_ZAen
dc.subjectNonlinear functional analysis.en
dc.subjectTheses--Mathematics.en
dc.titleDegree theory in nonlinear functional analysis.en
dc.typeThesisen


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