THE BROUWER DEGREE ASSOCIATED TO CLASSICAL EIGENVALUE PROBLEMS AND APPLICATIONS TO NONLINEAR SPECTRAL THEORY

Thanks to a connection between two completely different topics, the classical eigenvalue problem in a finite dimensional real vector space and the Brouwer degree for maps between oriented differentiable real manifolds, we are able to solve, at least in the finite dimensional context, a conjecture regarding global continuation in nonlinear spectral theory that we formulated in some recent papers. The infinite dimensional case seems nontrivial, and is still unsolved.