Homotopy and Degree Theory
For almost a century, degree theory has been a very important tool in analysis of existence and multiplicity results for solutions to nonlinear equations in euclidean spaces and manifolds. For example, the study of ordinary and partial differential equations has been considerably improved by degree theory. From the point of view taken in the present chapter, we give a simplified account of the matter by saying that degree theory consists in giving an estimate of the number of solutions to the equation f (x) = y for a function f: M → N, where M and N are C 2 boundaryless manifolds and f is continuous.
KeywordsOpen Subset Open Neighborhood General Equilibrium Neighborhood Versus Tubular Neighborhood
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