Kybernetika pro materiálové vědy

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    Existence of solutions converging to zero for nonlinear delayed differential systems
    (Springer, 2015-11-17) Rebenda, Josef; Šmarda, Zdeněk
    We present a result about an interesting asymptotic property of real two-dimensional delayed differential systems satisfying certain sufficient conditions. We employ two previous results, which were obtained using a Razumikhin-type modification of the Wazewski topological method for retarded differential equations and the method of a Lyapunov-Krasovskii functional.
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    Solvability of a close to symmetric system of difference equations
    (Department of Mathematics, Texas State University, 2016-06-27) Stevič, Stevo; Iričanin, Bratislav; Šmarda, Zdeněk
    The problem of solvability of a close to symmetric product-type system of di erence equations of second order is investigated. Some recent results in the literature are extended.
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    Conditional oscillation of half-linear Euler-type dynamic equations on time scales
    (University of Szeged, 2015-02-18) Hasil, Petr; Vítovec, Jiří
    We investigate second-order half-linear Euler-type dynamic equations on time scales with positive periodic coefficients. We show that these equations are conditionally oscillatory, i.e., there exists a sharp borderline (a constant given by the coefficients of the given equation) between oscillation and non-oscillation of these equations. In addition, we explicitly find this so-called critical constant. In the cases that the time scale is reals or integers, our result corresponds to the classical results as well as in the case that the coefficients are replaced by constants and we take into account the linear equations. An example and corollaries are provided as well.
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    Exponential Stability of Linear Discrete Systems with Multiple Delays
    (Hindawi, 2018-08-01) Baštinec, Jaromír; Demchenko, Hanna; Diblík, Josef; Khusainov, Denys
    The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay $x\left( {k+1} \right)=Ax\left( k \right)+\sum_{i=1}^sB_ix\left( {k-m_i} \right)$, $k=0,1,\dots$ where $s\in \mathbb{N}$, $A$ and $B_i$ are square matrices and $m_i\in\mathbb{N}$. New criterion for exponential stability is proved by the Lyapunov method. An estimate of the norm of solutions is given as well and relations to the well-known results are discussed.
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    On a product-type system of difference equations of second order solvable in closed form
    (BioMed Central, 2015-10-12) Stevič, Stevo; Iričanin, Bratislav; Šmarda, Zdeněk
    Sufficient conditions for solving a system of difference equations of second order in closed form are given. Moreover, sufficient conditions for existence of periodic solutions and asymptotic stability of solutions are given as well.