Browsing by Author "Tuba Negesso"

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    Global Solution Theorems for Odes
    (Addis Ababa University, 2016-08) Tuba Negesso; Tadesse Abdi
    This thesis explores the globalization of the implicit function theorem (IFT) within the context of global solution theorems for ordinary differential equations (ODEs). Traditionally, the IFT provides powerful local results, but its global applicability has been less thoroughly examined. By extending the IFT to a global setting, this work develops new theoretical frameworks for understanding and solving ODEs on a broader scale. The study introduces generalized formulations of the IFT, derives significant global bifurcation results, and applies topological methods such as the Leray-Schauder degree to substantiate these results. Emphasis is placed on deriving conditions under which global solutions can be effectively analyzed and obtained.