Fučík spectrum for discrete systems: curves and their tangent lines
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43977170" target="_blank" >RIV/49777513:23520/25:43977170 - isvavai.cz</a>
Result on the web
<a href="https://www.tandfonline.com/doi/full/10.1080/03081087.2025.2579765" target="_blank" >https://www.tandfonline.com/doi/full/10.1080/03081087.2025.2579765</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/03081087.2025.2579765" target="_blank" >10.1080/03081087.2025.2579765</a>
Alternative languages
Result language
angličtina
Original language name
Fučík spectrum for discrete systems: curves and their tangent lines
Original language description
In this paper, we study the Fučík spectrum of a square matrix A and provide necessary and sufficient conditions for the existence of Fučík curves emanating from the point (λ, λ) with λ being a real eigenvalue of A. We extend recent results by Maroncelli (2024) and remove his assumptions on symmetry of A and simplicity of λ. We show that the number of Fučík curves can significantly exceed the multiplicity of λ and determine all the possible directions they can emanate in. We also treat the situation when the algebraic multiplicity of λ is greater than the geometric one and show that in such a case the Fučík curves can lose their smoothness and provide the slopes of their ‘one-sided tangent lines’. Finally, we offer two possible generalizations for the follow-up research: the situation off the diagonal and the Fučík spectrum of a general Fredholm operator on the Hilbert space with a lattice structure.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA22-18261S" target="_blank" >GA22-18261S: Nonlinear problems with non-standard diffusion</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear and Multilinear Algebra
ISSN
0308-1087
e-ISSN
1563-5139
Volume of the periodical
73
Issue of the periodical within the volume
18
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
3965-3981
UT code for WoS article
001608708500001
EID of the result in the Scopus database
2-s2.0-105020874751