Oscillation theory on hybrid time domains: Local oscillation
properties

J 2026

Oscillation theory on hybrid time domains: Local oscillation properties

ŠEPITKA, Peter; Roman ŠIMON HILSCHER a Vera M. ZEIDAN

Základní údaje

Originální název

Oscillation theory on hybrid time domains: Local oscillation properties

Autoři

ŠEPITKA, Peter; Roman ŠIMON HILSCHER a Vera M. ZEIDAN

Vydání

Journal of Differential Equations, Elsevier Inc, 2026, 0022-0396

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 2.300 v roce 2024

Označené pro přenos do RIV

Ano

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1016/j.jde.2025.114080

UT WoS

001669301800001

Klíčová slova anglicky

Canonical system; Symplectic system; Time scale; Generalized focal point; Sturm separation theorem; Comparative index

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 6. 2. 2026 14:32, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

In this paper we introduce a new approach suitable for studying the local oscillation properties of solutions to canonical systems defined on arbitrary hybrid time domains, also called general time scales. Such systems are known as symplectic or Hamiltonian systems on time scales. We define the notions of the local multiplicities of generalized left and right focal points for conjoined bases of the system and establish, among other results, a local version of the Sturm separation theorem. This result leads to a new concept in the oscillation theory on time scales, which we call the minimal multiplicity at the given point. We derive several properties of these minimal multiplicities with special focus on their zero value. Our analysis is based on the theory of comparative index and dual comparative index of two Lagrangian planes, which is introduced and applied for the first time in this paper to canonical systems on time scales. We also relate the local multiplicities of generalized focal points corresponding to two conjoined bases with the limit properties of the comparative index and the dual comparative index. This theory produces new results when also applied to matrix Jacobi systems arising in variational analysis over time scales or to second order Sturm–Liouville equations on time scales.

Návaznosti

GA23-05242S, projekt VaV

Název: Oscilační teorie na hybridních časových doménách s aplikacemi ve spektrální teorii a maticové analýze

Investor: Grantová agentura ČR, Oscilační teorie na hybridních časových doménách s aplikacemi ve spektrální a maticové analýze

Citovat

ŠEPITKA, Peter; Roman ŠIMON HILSCHER a Vera M. ZEIDAN. Oscillation theory on hybrid time domains: Local oscillation properties. Journal of Differential Equations. Elsevier Inc, 2026, roč. 457, March, s. 114080-114121. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2025.114080.

@article{2547119,
   author = {Šepitka, Peter and Šimon Hilscher, Roman and Zeidan, Vera M.},
   article_number = {March},
   doi = {https://doi.org/10.1016/j.jde.2025.114080},
   keywords = {Canonical system; Symplectic system; Time scale; Generalized focal point; Sturm separation theorem; Comparative index},
   language = {eng},
   issn = {0022-0396},
   journal = {Journal of Differential Equations},
   title = {Oscillation theory on hybrid time domains: Local oscillation properties},
   url = {https://www.sciencedirect.com/science/article/pii/S0022039625011076},
   volume = {457},
   year = {2026}
}

TY  - JOUR
ID  - 2547119
AU  - Šepitka, Peter - Šimon Hilscher, Roman - Zeidan, Vera M.
PY  - 2026
TI  - Oscillation theory on hybrid time domains: Local oscillation properties
JF  - Journal of Differential Equations
VL  - 457
IS  - March
SP  - 114080
EP  - 114080
PB  - Elsevier Inc
SN  - 00220396
KW  - Canonical system
KW  - Symplectic system
KW  - Time scale
KW  - Generalized focal point
KW  - Sturm separation theorem
KW  - Comparative index
UR  - https://www.sciencedirect.com/science/article/pii/S0022039625011076
N2  - In this paper we introduce a new approach suitable for studying the local oscillation properties of solutions to canonical systems defined on arbitrary hybrid time domains, also called general time scales. Such systems are known as symplectic or Hamiltonian systems on time scales. We define the notions of the local multiplicities of generalized left and right focal points for conjoined bases of the system and establish, among other results, a local version of the Sturm separation theorem. This result leads to a new concept in the oscillation theory on time scales, which we call the minimal multiplicity at the given point. We derive several properties of these minimal multiplicities with special focus on their zero value. Our analysis is based on the theory of comparative index and dual comparative index of two Lagrangian planes, which is introduced and applied for the first time in this paper to canonical systems on time scales. We also relate the local multiplicities of generalized focal points corresponding to two conjoined bases with the limit properties of the comparative index and the dual comparative index. This theory produces new results when also applied to matrix Jacobi systems arising in variational analysis over time scales or to second order Sturm–Liouville equations on time scales.
ER  -

ŠEPITKA, Peter; Roman ŠIMON HILSCHER a Vera M. ZEIDAN. Oscillation theory on hybrid time domains: Local oscillation properties. \textit{Journal of Differential Equations}. Elsevier Inc, 2026, roč.~457, March, s.~114080-114121. ISSN~0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2025.114080.

Přehled o publikaci