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

被引：0

作者：

Benevieri, Pierluigi ^{[1
]}

Calamai, Alessandro ^{[2
]}

Furi, Massimo ^{[3
]}

Pera, Maria Patrizia ^{[3
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil

[2] Univ Politecn Marche, Dipartimento Ingn Civile Edile & Architettura, Via Brecce Bianche, I-60131 Ancona, Italy

[3] Univ Firenze, Dipartimento Matemat & Informat Ulisse Dini, Via S Marta 3, I-50139 Florence, Italy

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2022年 / 59卷 / 2A期

关键词：

Eigenvalues; eigenvectors; nonlinear spectral theory; degree theory; PERTURBED FREDHOLM OPERATOR; UNIT EIGENVECTORS; GLOBAL CONTINUATION; PERSISTENCE;

D O I：

10.12775/TMNA.2021.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：499 / 523

页数：25

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