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  1. 10 Opuscula Mathematica
  2. 3 Demonstratio Mathematica
  3. 3 Fasciculi Mathematici
  4. 3 Journal of Applied Analysis
  5. 1 Commentationes Mathematicae
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  1. 3 El-Matary Bassant M.
  2. 2 Attia Emad R.
  3. 2 Benekas Vasileios
  4. 2 Stavroulakis Ioannis P.
  5. 1 Ateiwi A.
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  1. 1 2023
  2. 2 2022
  3. 1 2021
  4. 1 2019
  5. 2 2018
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1
Content available Oscillation conditions for difference equations with several variable delays
El-Matary Bassant M., El-Morshedy Hassan A., Benekas Vasileios, Stavroulakis Ioannis P.
Opuscula Mathematica
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2023
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Vol. 43, no. 6
789--801
EN
A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.
2
Content available New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments
Attia Emad R., El-Matary Bassant M., Chatzarakis George E.
Opuscula Mathematica
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2022
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Vol. 42, no. 6
769--791
EN
In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving lim sup, which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.
3
Content available New aspects for the oscillation of first-order difference equations with deviating arguments
Attia Emad R., El-Matary Bassant M.
Opuscula Mathematica
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2022
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Vol. 42, no. 3
393--413
EN
We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.
4
Content available Oscillation criteria for linear difference equations with several variable delays
Benekas Vasileios, Garab Abel, Kashkynbayev Ardak, Stavroulakis Ioannis P.
Opuscula Mathematica
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2021
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Vol. 41, no. 5
613--627
EN
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.
5
Content available Difference equations with impulses
Danca Marius, Feckan Michal, Pospisil Michal
Opuscula Mathematica
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2019
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Vol. 39, no. 1
5--22
EN
Difference equations with impulses are studied focussing on the existence of periodic or bounded orbits, asymptotic behavior and chaos. So impulses are used to control the dynamics of the autonomous difference equations. A model of supply and demand is also considered when Li-Yorke chaos is shown among others.
6
Content available On the stability of some systems of exponential difference equations
Psarros N., Papaschinopoulos G., Schinas C.J.
Opuscula Mathematica
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2018
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Vol. 38, no. 1
95--115
EN
In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
7
Content available remote Reconstruction of potential and boundary conditions for second order difference equations
Currie S., Love A.
Commentationes Mathematicae
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2018
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Vol. 58, No. 1/2
1--9
EN
Assume the eigenvalues and the weights are given for a difference boundary value problem and that the form of the boundary conditions at the endpoints is known. In particular, it is known whether the endpoints are fixed (i.e. Dirichlet or non-Dirichlet boundary conditions) or whether the endpoints are free to move (i.e. boundary conditions with affine dependence on the eigenparameter). This work illustrates how the potential as well as the exact boundary conditions can be uniquely reconstructed. The procedure is inductive on the number of unit intervals. This paper follows along the lines of S. Currie and A. Love, Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions, Quaestiones Mathematicae, 40 (2017), no. 7, 861-877. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in the above reference, an additional spectrum is required more often than was the case in the unique reconstruction of the potential alone.
8
Content available Oscillation of second order difference equation with a sub-linear neutral term
Dharuman C., Graef J. R., Thandapani E., Vidhyaa K. S.
Journal of Mathematics and Applications
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2017
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Vol. 40
59--67
EN
This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.
9
Anti-periodic solutions for a higher order difference equation with p-Laplacian
Kong L., Parsley J., Rizzo K., Russell N.
Journal of Applied Analysis
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2017
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Vol. 23, nr 2
111--125
EN
A higher order difference equation is studied. The equation is defined onℤand contains a p-Laplacian and both advance and retardation. Some criteria are established for the existence of infinitely many anti-periodic solutions of the equation. Several consequences of the main theorems are also included. Two examples are provided to illustrate the applicability of the results.
10
Content available Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian
Candito P., D'Agui G.
Opuscula Mathematica
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2014
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Vol. 34, no. 4
683--690
EN
In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete p-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.
11
Content available remote On the qualitative study of the nonlinear difference equation ...[wzór]
Zayed E. M. E., El-Moneam M. A.
Fasciculi Mathematici
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2013
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Nr 50
137--147
EN
In this paper, we investigate the global behavior of the following non-linear difference equation ...[wzór] where the coefficients α, β, y, p Є (0,∞) and σ, τ Є N and the initial conditions x-x, x0 x-ω are arbitrary positive real numbers, where ω = max {σ, τ}.
12
Content available remote On the dynamics of the recursive sequence ...[wzór]
Erdogan M. E., Cinar C.
Fasciculi Mathematici
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2013
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Nr 50
59--66
EN
In this paper, we investigate the global behavior of the difference equation ...[wzór] where β is a positive parameter and α, γ are non-negative parameters and non-negative initial conditions.
13
Content available remote Application of difference equations to certain tridiagonal matrices
Borowska J., Łacińska L., Rychlewska J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 3
15-20
EN
In this paper we present an application of second order homogeneous linear difference equations with constant coefficients to evaluate the determinant of tridiagonal matrices. Comparing the obtained results with a certain alternative approach [1] some formulae for the finite sum are derived.
14
Content available remote Numerical simulation of NO production in a pulverized coal fired furnace
Straka R., Makovička J., Beneš M.
Environment Protection Engineering
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2011
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Vol. 37, nr 2
13-22
EN
Behaviour of air-coal mixture has been described using the Navier-Stokes equations for the mixture of air and coal particles, accompanied by the turbulence model. The undergoing chemical reactions are described by the Arrhenius kinetics (reaction rate proportional to exp(-E/RT) ). Heat transfer via conduction and radiation has also been considered. The system of partial difference equations is discretized using the finite volume method and the advection upstream splitting method as the Riemann solver. The resulting ordinary differential equations are solved using the 4th order Runge-Kutta method. Results of simulation for typical power production level are presented together with the air staging impact on NO production.
15
Content available On the global attractivity and the periodic character of a recursive sequence
Elsayed E. M.
Opuscula Mathematica
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2010
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Vol. 30, no. 4
431-446
EN
In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence [formula], where the parameters a, b, c, d and e are positive real numbers and the initial conditions x-2, x-1 and x0 are positive real numbers.
16
Content available remote Euler approximations can destroy unbounded solutions
Guy R. T., Misiurewicz M.
Fasciculi Mathematici
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2010
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Nr 44
43-52
EN
We show that there are ordinary differential equations in Rd with unbounded solutions, for which the difference equations obtained by using the forward Euler method have all solutions bounded.
17
Content available Solution of infinite slab static problem using the finite strip method by difference equations
Pawlak Z., Rakowski J.
Journal of Theoretical and Applied Mechanics
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2009
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Vol. 47 nr 3
629-643
EN
An analytical approach to the solution of an infinite slab static problem using the finite strip method is presented. The structure simply supported on its opposite edges is treated as a discrete one. A regular mesh of identical finite strips approximates the continuous structure. This regular slab discretization enables one to derive a fundamental solution for the two-dimensional discrete strip structure in an analytical, closed form. Equilibrium conditions are derived from the finite element method formulation. The set of the infinite number of equilibrium conditions is replaced by one equivalent difference equation. The solution to this equation is the fundamental function, i.e. Green's function for considered slab strip.
PL
W pracy zaprezentowano analityczne rozwiązanie problemu statyki nieograniczonej tarczy metodą pasm skończonych. Tarcza swobodnie podparta na przeciwległych krawędziach jest rozwiązywana jako układ dyskretny. Ciągła struktura jest aproksymowana regularną siatką składającą się z identycznych pasm skończonych. Regularny podział pozwala na wyprowadzenie funkcji fundamentalnych dla dwuwymiarowego układu dyskretnego w analitycznej, zamkniętej formie. Warunki równowagi zostały wyprowadzone zgodnie ze sformułowaniem metody elementów skończonych. Układ równań równowagi składający się z nieskończonej liczby równań został zastąpiony jednym, równoważnym równaniem różnicowym. Rozwiązanie tego równania jest funkcją fundamentalną dla rozpatrywanej tarczy.
18
Content available remote Oscillation criteria for higher order functional difference equation with oscillating coeffcient
Bolat Y.
Demonstratio Mathematica
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2007
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Vol. 40, nr 1
161-168
EN
In this paper we are concerned with the oscillatory behaviour of solutions of a certain higher order nonlinear neutral type functional difference equation with oscillating coefficient. We obtain two sufficient criteria for oscillatory behaviour.
19
Content available Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences
Schmeidel E.
Opuscula Mathematica
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2006
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Vol. 26, no. 2
361-369
EN
In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.
20
Content available On oscillatory solutions of certain difference equations
Grzegorczyk G., Werbowski J.
Opuscula Mathematica
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2006
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Vol. 26, no. 2
317-326
EN
Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
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