Vysoké učení technické v Brně, Fakulta stavební,
Ústav matematiky a deskriptivní geometrie
Vás zve na přednášku

On the symmetry in sharp oscillation criteria for second-order functional differential equations

Úterý 2. prosince 2025 ve 10:00

 

Abstract. We study the oscillation of second-order half-linear functional differential equations under two fundamental dichotomies: the nature of deviating argument (delay vs. advance) and Trench’s canonical classification (canonical vs. non-canonical form). For each of the four resulting cases, sharp extensions of the classical Hille–Kneser oscillation criterion are obtained via an iterative monotonicity method. These criteria exhibit a notable symmetry: the canonical delay case pairs with the non-canonical advance case and vice versa for the canonical advance and non-canonical delay cases. We conclude by discussing possible extensions of the results to higher-order functional differential equations.

 

v zasedací místnosti ústavu (2. patro Z205), ul. Žižkova 17.

Přednášku přednese dr. Irena Jadlovská,

Mathematical Institute, Slovak Academy of Science, extension in Košice, Košice, Slovak Republic

 

Přednáška je určena všem zájemcům o problematiku.

 

Ing. Jan Holešovský, Ph.D.

vedoucí ÚMDG

 

Leták

 

Vysoké učení technické v Brně, Fakulta stavební,
Ústav matematiky a deskriptivní geometrie
Vás zve na přednášku

On the Complexification of Linear Operators and its Applications

Středa 11. listopadu 2025 ve 14:15

 

Abstract. The aim of this talk is to demonstrate how the complexification procedure can be used to derive important properties of operators acting on a real Hilbert space from their counterparts in the complex setting. In particular, we will outline how the spectral representation theorem for real Hilbert spaces can be derived from its complex version. Although this result is often regarded as part of mathematical folklore, it nonetheless requires some explanation.

 

v zasedací místnosti ústavu (2. patro Z205), ul. Žižkova 17.

Přednášku přednese dr. Witold Majdak,

Department of Mathematical Analysis and Applications, Faculty of Applied Mathematics, AGH University of Krakow, Krakow, Poland

 

Přednáška je určena všem zájemcům o problematiku.

 

Ing. Jan Holešovský, Ph.D.

vedoucí ÚMDG

 

Leták

 

Vysoké učení technické v Brně, Fakulta stavební,
Ústav matematiky a deskriptivní geometrie
Vás zve na přednášku

Shadowing and hyperbolicity for linear delay difference equations

Středa 27. srpna 2025 ve 13:00

 

Abstract. It is known that hyperbolic linear delay difference equations are shadowable on the half-line. In this talk, we prove the converse and hence the equivalence between hyperbolicity and the positive shadowing property for the following two classes of linear delay difference equations: (a) for non-autonomous equations with finite delays and uniformly bounded compact coefficient operators in Banach spaces, (b) for Volterra difference equations with infinite delay in finite dimensional spaces.

 

v zasedací místnosti ústavu (2. patro Z205), ul. Žižkova 17.

Přednášku přednese prof. Mihály Pituk,

Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary

 

Přednáška je určena všem zájemcům o problematiku.

 

Ing. Jan Holešovský, Ph.D.

vedoucí ÚMDG

 

Leták

 

Vysoké učení technické v Brně, Fakulta stavební,
Ústav matematiky a deskriptivní geometrie
Vás zve na přednášku

On the Systems of Nonlinear Evolution Equations – Existence and Uniqueness vie Theory of M-Matrices

Úterý 5. listopadu 2024 ve 12:30

 

Abstract. A system of nonlinear evolution equations with strictly monotone operators and perturbations satisfying certain counterpart of one-sided Lipschitz condition is considered. To reach the existence and uniqueness result, a certain remetrization method is proposed based on M-matrices theory and utilizing the Gelfand triple setting, which enables usage of a certain type of relaxed monotonicity. Asymptotic properties of the solution are also investigated by showing that any solution tends to the solution of a stationary problem. The results obtained are illustrated by considering a system of equations involving (q,p)-Laplacians and suitable non-monotone perturbations.

 

v zasedací místnosti ústavu (2. patro Z205), ul. Žižkova 17.

Přednášku přednese Dr. Michał Bełdziński,

Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary

 

Přednáška je určena všem zájemcům o problematiku.

 

Ing. Jan Holešovský, Ph.D.

vedoucí ÚMDG

 

Leták

 

Vysoké učení technické v Brně, Fakulta stavební,
Ústav matematiky a deskriptivní geometrie
Vás zve na přednášku

Shadowing, Hyers-Ulam stability and hyperbolicity for nonautonomous linear delay differential equations

Středa 28. srpna 2024 ve 13:00

 

Abstract. It is known that hyperbolic nonautonomous linear delay differential equations in finite dimensional spaces are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this talk, we show the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the uniform boundedness assumption will be shown by an example.

 

This is a joint work with Professors Lucas Backes (Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil) and Davor Dragičević (University of Rijeka, Rijeka, Croatia).

 

v zasedací místnosti ústavu (2. patro Z205), ul. Žižkova 17.

Přednášku přednese prof. Mihály Pituk,

Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary

 

Přednáška je určena všem zájemcům o problematiku.

 

Ing. Jan Holešovský, Ph.D.

vedoucí ÚMDG

 

Leták