A degree associated to linear eigenvalue problems in Hilbert spaces and applications to nonlinear spectral theory
Spectral Theory
2021-01-08 v2
Abstract
We extend to the infinite dimensional context the link between two completely different topics recently highlighted by the authors: the classical eigenvalue problem for real square matrices and the Brouwer degree for maps between oriented finite dimensional real manifolds. Thanks to this extension, we solve a conjecture regarding global continuation in nonlinear spectral theory that we have formulated in a recent article. Our result (the ex conjecture) is applied to prove a Rabinowitz type global continuation property of the solutions to a perturbed motion equation containing an air resistance frictional force.
Cite
@article{arxiv.2006.15539,
title = {A degree associated to linear eigenvalue problems in Hilbert spaces and applications to nonlinear spectral theory},
author = {Pierluigi Benevieri and Alessandro Calamai and Massimo Furi and Maria Patrizia Pera},
journal= {arXiv preprint arXiv:2006.15539},
year = {2021}
}