By Patrick Fitzpatrick
The purpose of this paintings is to boost an additive, integer-valued measure conception for the category of quasilinear Fredholm mappings. This category is adequately huge that, inside of its framework, one can research normal totally nonlinear elliptic boundary worth difficulties. a level for the complete category of quasilinear Fredholm mappings needs to unavoidably accomodate sign-switching of the measure alongside admissible homotopies. The authors introduce "parity", a homotopy invariant of paths of linear Fredholm operators having invertible endpoints. The parity presents a whole description of the prospective alterations in signal of the measure and thereby allows use of the measure to turn out multiplicity and bifurcation theorems for quasilinear Fredholm mappings. functions are given to the learn of absolutely nonlinear elliptic boundary price difficulties.
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