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.

A degree associated to linear eigenvalue problems in Hilbert spaces and applications to nonlinear spectral theory / PIERLUIGI BENEVIERI, ALESSANDRO CALAMAI, MASSIMO FURI, MARIA PATRIZIA PERA. - In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. - ISSN 1040-7294. - STAMPA. - 34:(2022), pp. 555-581. [10.1007/s10884-020-09921-9]

A degree associated to linear eigenvalue problems in Hilbert spaces and applications to nonlinear spectral theory

MARIA PATRIZIA PERA
2022

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.
2022
34
555
581
Goal 17: Partnerships for the goals
PIERLUIGI BENEVIERI, ALESSANDRO CALAMAI, MASSIMO FURI, MARIA PATRIZIA PERA
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1204859
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