Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2019
Volume
Vol. 39
Number
No. 1
Description
Journal Volume
Opuscula Mathematica
Vol. 39 (2019)
Projects
Pages
Articles
Difference equations with impulses
(Wydawnictwa AGH, 2019) Danca, Marius; Fečkan, Michal; Pospíšil, Michal
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.
Dynamic system with random structure for modeling security and risk management in cyberspace
(Wydawnictwa AGH, 2019) Džalladova, Ìrada Agaêvna; Růžičková, Miroslava
We deal with the investigation of $L_{2}$-stability of the trivial solution to the system of difference equations with coefficients depending on a semi-Markov chain. In our considerations, random transformations of solutions are assumed. Necessary and sufficient conditions for $L_{2}$-stability of the trivial solution to such systems are obtained. A method is proposed for constructing Lyapunov functions and the conditions for its existence are justified. The dynamic system and methods discussed in the paper are very well suited for use as models for protecting information in cyberspace.
Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term
(Wydawnictwa AGH, 2019) Graef, John R.; Grace, Said R.; Tunç, Ercan
The authors present a new technique for the linearization of even-order nonlinear differential equations with a sublinear neutral term. They establish some new oscillation criteria via comparison with higher-order linear delay differential inequalities as well as with first-order linear delay differential equations whose oscillatory characters are known. Examples are provided to illustrate the theorems.
Boundary value problems with solutions in convex sets
(Wydawnictwa AGH, 2019) Herzog, Gerd; Kunstmann, Peer Christian
By means of the continuation method for contractions we prove the existence of solutions of Dirichlet boundary value problems in convex sets. As an application we prove the existence of concave solutions of certain boundary value problems in ordered Banach spaces.
On the convergence of solutions to second-order neutral difference equations
(Wydawnictwa AGH, 2019) Migda, Małgorzata; Migda, Janusz; Zdanowicz, Małgorzata
A second-order nonlinear neutral difference equation with a quasi-difference is studied. Sufficient conditions are established under which for every real constant there exists a solution of the considered equation convergent to this constant.