Contributions to Generalized Oscillation Theory of Linear Hamiltonian Systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139566" target="_blank" >RIV/00216224:14310/24:00139566 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00025-024-02280-7" target="_blank" >https://link.springer.com/article/10.1007/s00025-024-02280-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-024-02280-7" target="_blank" >10.1007/s00025-024-02280-7</a>
Alternative languages
Result language
angličtina
Original language name
Contributions to Generalized Oscillation Theory of Linear Hamiltonian Systems
Original language description
In this paper we present several new contributions to the oscillation theory of linear differential equations, in particular of linear Hamiltonian systems, when the traditional Legendre condition is absent. Following our recent work (Discrete Contin. Dyn. Syst. 43(12):4139–4173, 2023), we introduce the multiplicity of a generalized right focal point and derive the corresponding local Sturmian separation theorem. We also examine the relation between the existence of finitely many generalized right focal points, or in the special case the nonexistence of generalized right focal points, with the Legendre condition. As the main tools we use new notions of the minimal multiplicities at a given point and the dual comparative index — an object from matrix analysis or differential geometry (Maslov index theory). Furthermore, we study local limit properties of the dual comparative index and the comparative index and apply them for deriving new oscillation results phrased in terms of the generalized right and left focal points. The investigation of the interplay between generalized right and left focal points leads to conditions characterizing the situation, when in the local Sturmian separation theorem the corresponding multiplicities attain the minimal possible value. This also provides a generalization of the concepts of the right and left proper focal point defined by Kratz (Analysis 23(2):163–183, 2003) and Wahrheit (Int. J. Differ. Equ. 2(2):221–244, 2007) to the setting, which does not impose the Legendre condition. The results are new even for completely controllable linear Hamiltonian systems, including the Sturm–Liouville differential equations of arbitrary even order.
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/GA23-05242S" target="_blank" >GA23-05242S: Oscillation theory on hybrid time domains with applications in spectral theory and matrix analysis</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Results in Mathematics
ISSN
1422-6383
e-ISSN
1420-9012
Volume of the periodical
79
Issue of the periodical within the volume
8
Country of publishing house
SE - SWEDEN
Number of pages
47
Pages from-to
1-47
UT code for WoS article
001338514400001
EID of the result in the Scopus database
2-s2.0-85207494747