This article is only in Czech.

Vedoucí semináře:

• Prof. RNDr. Zuzana Došlá, DSc.
  
• Prof. RNDr. Roman Šimon Hilscher, DSc.

Archiv minulých seminářů

Tradiční seminář o diferenciálních rovnicích se koná (obvykle) každé pondělí od 12:00 do 13:30 v zasedací místnosti (první patro ihned naproti schodům) Ústavu matematiky a statistiky (budova č. 8) v areálu Přírodovědecké fakulty (Kotlářská 2). Neobsazené termíny přednášek jsou průběžně doplňovány. V jednání jsou přednášky účastníků našeho semináře a dalších hostů ze zahraničí.

Program semináře v akademickém roce 2025/2026

1. 12. 2025, 12:00 [zasedací místnost ÚMS PřF MU]

doc. RNDr. Karel Hasík, Ph.D. (Matematický ústav v Opavě, Slezská univerzita)

Global stability of Wright-type equations with negative Schwarzian.

Abstrakt
Simplicity of the 37/24-global stability criterion announced by E.M. Wright in 1955 and rigorously proved by B. Bánhelyi et al in 2014 for the delayed logistic equation raised the question of its possible extension for other population models. In our study, we answer this question by extending the 37/24-stability condition for the Wright-type equations with decreasing smooth nonlinearity \(f\) which has a negative Schwarzian and satisfies the standard negative feedback and boundedness assumptions. The proof contains the construction and careful analysis of qualitative properties of certain bounding relations. To validate our conclusions, these relations are evaluated at finite sets of points; for this purpose, we systematically use interval analysis.

3. 11. 2025, 12:00 [zasedací místnost ÚMS PřF MU]

Satyam Narayan Srivastava, MSc, Ph.D. (Ústav matematiky a statistiky, PřF MU)

Existence of solution for fractional boundary value problems by coincidence degree theory.

Abstrakt
This talk presents recent developments in the use of coincidence degree theory for nonlinear fractional differential equations. The focus is on the existence of solutions to higher-order Riemann–Liouville fractional differential equations with Riemann–Stieltjes integral boundary conditions at resonance. These boundary conditions extend and unify several classical cases studied in the literature. Further results for fractional boundary value problems involving the Caputo, Hadamard, and Katugampola derivatives are also discussed.

20. 10. 2025, 12:00 [zasedací místnost ÚMS PřF MU]

doc. Mgr. Diana Schneiderová, Ph.D. (Katedra matematiky, PřF OU)

Influence of the magnetic field on the discrete spectrum of Schroedinger operator under domain perturbation.

Abstrakt
For a two-dimensional curved waveguide, it is well known that the spectrum of the Dirichlet Laplacian is unstable. Any perturbation of the straight strip produces eigenvalues below the essential spectrum. In this work, a magnetic field is added. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small but non-local deformations of the waveguide.
The next part of work is devoted to the magnetic Schroedinger operator with a non-negative potential supported over a strip which is a local deformation of a straight one, and the magnetic field is assumed to be nonzero and local. We show that the magnetic field does not change the essential spectrum of this system, and investigate a sufficient condition for the discrete spectrum of operator to be empty.

29. 9. 2025, 12:00 [zasedací místnost ÚMS PřF MU]

prof. RNDr. Roman Šimon Hilscher, DSc. (Ústav matematiky a statistiky, PřF MU)

New results related to disconjugacy of linear Hamiltonian systems.