Browsing Ústav matematiky by Issue Date
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Asymptotic convergence of the solutions of a dynamic equation on discrete time scales
(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 ... 
Solving certain classes of LaneEmden type equations using differential transformation method
(Springer Nature, 20121005)In this paper, differential transformation method (DTM) is applied to solve singular initial problems represented by certain classes of LaneEmden type equations. Some new differential tranformation formulas for certain ... 
Bounded solutions of delay dynamic equations on time scales
(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 ... 
Stabilization of Luretype Nonlinear Control Systems by LyapunovKrasovskii Functionals
(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 ... 
An efficient new perturbative Laplace method for spacetime fractional telegraph equations
(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. 
Singular Initial Value Problem for a System of IntegroDifferential Equations
(Hindawi, 20121212)Analytical properties like existence, uniqueness, and asymptotic behavior of solutions are studied for the singular initial value problem. An approach which combines topological method of T. Wazewski and Schauders fixed ... 
On a delay population model with quadratic nonlinearity
(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 ... 
Explicit general solution of planar linear discrete systems with constant coefficients and weak delays
(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 $k\in\bZ_0^{\infty}:=\{0,1,\dots,\infty\}$, $x\colon \bZ_0^{\infty}\to\mathbb{R}^2$, ... 
Discrete matrix delayed exponential for two delays and its property
(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 ... 
Modeling of applied problems by stochastic systems and their analysis using the moment equations
(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 ... 
NewtonKantorovich convergence theorem of a new modified Halleys method family in a Banach space
(Springer, 20131112)A NewtonKantorovich convergence theorem of a new modified Halleys method family is established in a Banach space to solve nonlinear operator equations 
Stabilization of company’s income modeled by a system of discrete stochastic equations
(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 ... 
On a producttype system of difference equations of second order solvable in closed form
(BioMed Central, 20151012)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 ... 
Bounded and unbounded nonoscillatory solutions of a fourdimensional nonlinear neutral difference system
(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 ... 
Existence of solutions converging to zero for nonlinear delayed differential systems
(Springer, 20151117)We present a result about an interesting asymptotic property of real twodimensional delayed differential systems satisfying certain sufficient conditions. We employ two previous results, which were obtained using a ... 
Boundedness character of a fourthorder system of difference equations
(Springer Nature, 20151201)Sufficient conditions for boundedness character of solutions of a fourthorder system of difference equations is given. 
On a close to symmetric system of difference equations of second order
(Springer Nature, 20151229)Closed form formulas of the solutions to the system of difference equations of the second order are found. The domain of undefinable solutions to the system is described. 
Exponential stability of perturbed linear discrete systems
(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 ... 
Twodimensional producttype system of difference equations solvable in closed form
(Springer Nature, 20161003)A solvable twodimensional producttype system of difference equations of interest is presented. Closed form formulas for its general solution are given. 
Modelling precipitation extremes in the Czech Republic: Update of intensitydurationfrequency curves
(Estonian Academy Publishers, 20161220)Precipitation records from six stations of the Czech Hydrometeorological Institute were subject to statistical analysis with the objectives of updating the IntensityDurationFrequency (IDF) curves, by applying extreme ...