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Dissertation
Results and Examples Regarding Bifurcation with a Two-Dimensional Kernal
Scholarship and Professional Work - LAS
  • Scott R. Kaschner, Butler University
Document Type
Dissertation
Publication Date
1-1-2008
Disciplines
Abstract
Many problems in pure and applied mathematics entail studying the structure of solutions to F(x; y) = 0, where F is a nonlinear operator between Banach spaces and y is a real parameter. A parameter value where the structure of solutions of F changes is called a bifurcation point. The particular method of analysis for bifurcation depends on the dimension of the kernel of DxF(0,λ), the linearization of F. The purpose of our study was to examine some consequences of a recent theorem on bifurcations with 2-dimensional kernels. This resent theorem was compared to previous methods. Also, some specific classes of equations were identified in which the theorem always holds, and an algebraic example was found that illustrates bifurcations with a 2-dimensional kernel.
Rights

This is an electronic copy of a Masters Thesis. Archived with permission. © Scott Kaschner, 2008. The author reserves all rights.

Citation Information
Scott R. Kaschner. "Results and Examples Regarding Bifurcation with a Two-Dimensional Kernal" (2008) - 74
Available at: http://works.bepress.com/scott-kaschner/12/