Comparable to the importance of the Implicit Function Theorem for the local analysis is the degree of a mapping for any global analysis. Although the theory was originally invented and defined in topology we present an analytical theory developed later. For finite-dimensional continuous mappings it is the Brouwer degree; its extension to infinite dimensions is the Leray–Schauder degree.
KeywordsFredholm Operator Morse Index Global Theory Algebraic Multiplicity Compact Perturbation
Unable to display preview. Download preview PDF.