Browsing Ústav matematiky by Author "Diblík, Josef"
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Asymptotic convergence of the solutions of a dynamic equation on discrete time scales
Diblík, Josef; Růžičková, Miroslava; Šmarda, Zdeněk; Šutá, Zuzana (Hindawi, 20120103)It is proved that, for the asymptotic convergence of all solutions, the existence of an increasing and asymptotically convergent solution is sufficient. Therefore, the main attention is paid to the criteria for the existence ... 
Bounded and unbounded nonoscillatory solutions of a fourdimensional nonlinear neutral difference system
Diblík, Josef; Lupinska, Barbara; Růžičková, Miroslava; Zonenberg, Joanna (Springer Nature, 20151015)The paper is concerned with a fourdimensional nonlinear difference system with delayed arguments where the first equation of the system is of a neutral type. A classification of nonoscillatory solutions is given and ... 
Bounded solutions of delay dynamic equations on time scales
Diblík, Josef; Vítovec, Jiří (Springer Nature, 20121024)In this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where $f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$ is a ... 
Discrete matrix delayed exponential for two delays and its property
Diblík, Josef; Morávková, Blanka (Springer Nature, 20130613)In recent papers, a discrete matrix delayed exponential for a single delay was defined and its main property connected with the solution of linear discrete systems with a single delay was proved. In the present paper, a ... 
An efficient new perturbative Laplace method for spacetime fractional telegraph equations
Khan, Yasir; Diblík, Josef; Faraz, Naeem; Šmarda, Zdeněk (Springer Nature, 20121127)In this paper, we propose a new technique for solving spacetime fractional telegraph equations. This method isbased on perturbation theory and the Laplace transformation. 
Explicit general solution of planar linear discrete systems with constant coefficients and weak delays
Diblík, Josef; Halfarová, Hana (Springer Nature, 20130306)In this paper, planar linear discrete systems with constant coefficients and two delays $$ x(k+1)=Ax(k)+Bx(km)+Cx(kn) $$ are considered where $k\in\bZ_0^{\infty}:=\{0,1,\dots,\infty\}$, $x\colon \bZ_0^{\infty}\to\mathbb{R}^2$, ... 
Exponential stability of perturbed linear discrete systems
Diblík, Josef; Khusainov, Denys; Baštinec, Jaromír; Sirenko, Andrii (Springer, 20160129)The paper considers the problem of exponential stability and convergence rate to solutions of perturbed linear discrete homogeneous systems. New criteria on exponential stability are derived by using the second method of ... 
Lower and upper estimates of solutions to systems of delay dynamic equations on time scales
Diblík, Josef; Vítovec, Jiří (Springer, 20131127)In this paper we study a system of delay dynamic equations on the time scale $\T$ of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_ ... 
Modeling of applied problems by stochastic systems and their analysis using the moment equations
Diblík, Josef; Dzhalladova, Irada; Michalková, Mária; Růžičková, Miroslava (Springer Nature, 20131009)The paper deals with systems of linear differential equations with coefficients depending on the Markov process. Equations for particular density and the moment equations for given systems are derived and used in the ... 
On a delay population model with quadratic nonlinearity
Berezansky, Leonid; Baštinec, Jaromír; Diblík, Josef; Šmarda, Zdeněk (Springer Nature, 20121228)In this paper, a nonlinear delay differential equation with quadratic nonlinearity is investigated. It is proved that the positive equilibrium is globally asymptotically stable without any further limitations on parameters ... 
Stabilization of company’s income modeled by a system of discrete stochastic equations
Diblík, Josef; Dzhalladova, Irada; Růžičková, Miroslava (Springer Nature, 20141115)The paper deals with a system of difference equations where the coefficients depend on Markov chains. The functional equations for a particular density and the moment equations for the system are derived and used in the ... 
Stabilization of Luretype Nonlinear Control Systems by LyapunovKrasovskii Functionals
Shatyrko, Andrej; Diblík, Josef; Khusainov, Denys; Růžičková, Miroslava (Springer Nature, 20121024)The paper deals with the stabilization problem of Luretype nonlinear indirect control systems with timedelay argument. The sufficient conditions for absolute stability of the control system are established in the form ...