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

11. 5. 2026, 12:00 [zasedací místnost ÚMS PřF MU]

Mgr. Ludmila Linhartová (Ústav matematiky a statistiky, PřF MU)

Oscillation criterion for generalized Euler difference equations.

27. 4. 2026, 12:00 [zasedací místnost ÚMS PřF MU]

doc. RNDr. Milan Tvrdý, CSc. (Matematický ústav, AV ČR)

Periodic problems with space singularities.

13. 4. 2026, 12:00 [zasedací místnost ÚMS PřF MU]

prof. RNDr. Jan Čermák, CSc. (Ústav matematiky, FSI VUT Brno)

Lambert function, its properties and use in the theory of delay differential equations.

30. 3. 2026, 12:00 [zasedací místnost ÚMS PřF MU]

doc. Mgr. Peter Šepitka, Ph.D. (Ústav matematiky a statistiky, PřF MU)

A new formula for multiplicities of focal points in discrete oscillation theory.

16. 3. 2026, 12:00 [zasedací místnost ÚMS PřF MU]

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

Inequalities for Fractional BVPs via Lyapunov-type approach and derived from the Vallée-Poussin Theorem.

Abstrakt
For Lyapunov inequalities, the main approach involves transforming the boundary value problem into an integral equation using Green’s function. By estimating the bounds of Green’s function, we can derive inequalities and discuss the existence of solutions. However, obtaining these estimates for many Green’s functions is not straightforward and requires rigorous analytical work. In this talk, we present two of our recent works on Caputo fractional boundary value problems, focusing on new results concerning Lyapunov-type inequalities.
In another work, we derived inequalities based on Vallée-Poussin theorem through three assertions for the fractional functional differential equation. We will discuss our recent results for different class of fractional boundary value problem with different definitions of fractional derivatives. This theorem addresses the existence, uniqueness and positivity of solutions. We obtain necessary and sufficient conditions of negativity of Green’s function to problem in form of assertion about differential inequality.

9. 3. 2026, 12:00 [zasedací místnost ÚMS PřF MU]

prof. RNDr. Zuzana Došlá, DSc. (Ústav matematiky a statistiky, PřF MU)

Radial solutions to equation with regularly varying operator.

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.