Opuscula Mathematica
Loading...
ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2021
Volume
Vol. 41
Number
No. 5
Description
Journal Volume
Opuscula Mathematica
Vol. 41 (2021)
Projects
Pages
Articles
Oscillation criteria for linear difference equations with several variable delays
(Wydawnictwa AGH, 2021) Benekas, Vasileios; Garab, Ábel; Kashkynbayev, Ardak; Stavroulakis, Ioannis P.
We obtain new sufficient criteria for the oscillation of all solutions of linear delay difference equations with several (variable) finite delays. Our results relax numerous well-known limes inferior-type oscillation criteria from the literature by letting the limes inferior be replaced by the limes superior under some additional assumptions related to slow variation. On the other hand, our findings generalize an oscillation criterion recently given for the case of a constant, single delay.
Extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm
(Wydawnictwa AGH, 2021) Boulahia, Fatiha; Hassaine, Slimane
In the present paper, we give criteria for the existence of extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm. Some properties of the set of attainable points of the Amemiya norm in this space are also discussed.
Closed range weighted composition operators between Lp-spaces
(Wydawnictwa AGH, 2021) Lo, Ching-on; Loh, Anthony Wai-keung
We characterize the closedness of ranges of weighted composition operators between $L^p$-spaces, where $1 \leq p \leq \infty$. When the $L^p$-spaces are weighted sequence spaces, several corollaries about this class of operators are also deduced.
Coboundaries of commuting Borel automorphisms
(Wydawnictwa AGH, 2021) Sanadhya, Shrey
We show that if $S$, $T$ are two commuting automorphisms of a standard Borel space such that they generate a free Borel $\mathbb{Z}^{2}$-action then $S$ and $T$ do not have same sets of real valued bounded coboundaries. We also prove a weaker form of Rokhlin Lemma for Borel $\mathbb{Z}^{d}$-actions.
On classical symmetries of ordinary differential equations related to stationary integrable partial differential equations
(Wydawnictwa AGH, 2021) Tsyfra, Ivan
We study the relationship between the solutions of stationary integrable partial and ordinary differential equations and coefficients of the second-order ordinary differential equations invariant with respect to one-parameter Lie group. The classical symmetry method is applied. We prove that if the coefficients of ordinary differential equation satisfy the stationary integrable partial differential equation with two independent variables then the ordinary differential equation is integrable by quadratures. If special solutions of integrable partial differential equations are chosen then the coefficients satisfy the stationary KdV equations. It was shown that the Ermakov equation belong to a class of these equations. In the framework of the approach we obtained the similar results for generalized Riccati equations. By using operator of invariant differentiation we describe a class of higher order ordinary differential equations for which the group-theoretical method enables us to reduce the order of ordinary differential equation.