Oscillation theory on hybrid time domains: Global oscillation
properties

J 2026

Oscillation theory on hybrid time domains: Global oscillation properties

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

Základní údaje

Originální název

Oscillation theory on hybrid time domains: Global 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

Klíčová slova anglicky

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

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 18. 5. 2026 07:38, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

In this paper we investigate global oscillation properties of solutions to canonical differential systems on arbitrary hybrid time domains (time scales). We use the concepts of generalized left and right focal points for solutions defined on hybrid time domains, which we introduced and developed in our previous paper, in order to derive the Sturm separation theorems on a given time scale interval. These separation theorems are new even for matrix Jacobi systems arising in the optimal control problems on time scales or for the second order Sturm–Liouville equations on time scales. We utilize the comparative index theory of two Lagrangian planes as a key tool to study the global nonexistence of generalized left and right focal points, the monotonicity properties of the comparative index involving two solutions of the system, and the mutual relations between the numbers of generalized left and right focal points. We also consider the minimal multiplicities at left-dense and right-dense points and the strengthened Legendre condition to establish additional new results in this subject. The presented theory unifies and extends the global oscillation (Sturm–type) results known in the special cases of continuous time linear Hamiltonian differential systems and discrete time symplectic difference systems.

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: Global oscillation properties. Journal of Differential Equations. Elsevier Inc., 2026, roč. 472, August, s. 1-48. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2026.114424.

@article{2569222,
   author = {Šepitka, Peter and Šimon Hilscher, Roman and Zeidan, Vera M.},
   article_number = {August},
   doi = {https://doi.org/10.1016/j.jde.2026.114424},
   keywords = {Canonical system; Time scale; Generalized focal point; Sturm separation theorem; Comparative index; Matrix Jacobi system},
   language = {eng},
   issn = {0022-0396},
   journal = {Journal of Differential Equations},
   title = {Oscillation theory on hybrid time domains: Global oscillation properties},
   url = {https://www.sciencedirect.com/science/article/pii/S0022039626003311},
   volume = {472},
   year = {2026}
}

TY  - JOUR
ID  - 2569222
AU  - Šepitka, Peter - Šimon Hilscher, Roman - Zeidan, Vera M.
PY  - 2026
TI  - Oscillation theory on hybrid time domains: Global oscillation properties
JF  - Journal of Differential Equations
VL  - 472
IS  - August
SP  - 1-48
EP  - 1-48
PB  - Elsevier Inc.
SN  - 00220396
KW  - Canonical system
KW  - Time scale
KW  - Generalized focal point
KW  - Sturm separation theorem
KW  - Comparative index
KW  - Matrix Jacobi system
UR  - https://www.sciencedirect.com/science/article/pii/S0022039626003311
N2  - In this paper we investigate global oscillation properties of solutions to canonical differential systems on arbitrary hybrid time domains (time scales). We use the concepts of generalized left and right focal points for solutions defined on hybrid time domains, which we introduced and developed in our previous paper, in order to derive the Sturm separation theorems on a given time scale interval. These separation theorems are new even for matrix Jacobi systems arising in the optimal control problems on time scales or for the second order Sturm–Liouville equations on time scales. We utilize the comparative index theory of two Lagrangian planes as a key tool to study the global nonexistence of generalized left and right focal points, the monotonicity properties of the comparative index involving two solutions of the system, and the mutual relations between the numbers of generalized left and right focal points. We also consider the minimal multiplicities at left-dense and right-dense points and the strengthened Legendre condition to establish additional new results in this subject. The presented theory unifies and extends the global oscillation (Sturm–type) results known in the special cases of continuous time linear Hamiltonian differential systems and discrete time symplectic difference systems.
ER  -

ŠEPITKA, Peter; Roman ŠIMON HILSCHER a Vera M. ZEIDAN. Oscillation theory on hybrid time domains: Global oscillation properties. \textit{Journal of Differential Equations}. Elsevier Inc., 2026, roč.~472, August, s.~1-48. ISSN~0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2026.114424.

Přehled o publikaci