Degree theory in nonlinear functional analysis.
| dc.contributor.advisor | Hill, C. K. | |
| dc.contributor.author | 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 | 1989 | |
| 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 [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.identifier.uri | http://hdl.handle.net/10413/9795 | |
| 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 |