Singular second-order multipoint dynamic boundary value problems with mixed derivatives.
Gronwall-OuIang-type integral inequalities on time scales.
Editorial: Dynamic equations and applications. Special issue dedicated to Professor Gusein Guseinov on the occasion of his 55th birthday.
Trench's perturbation theorem for dynamic equations.
Ostrowski inequalities on time scales.
The convolution on time scales.
Weyl-Titchmarsh theory for Hamiltonian dynamic systems.
Multiple Lebesgue integration on time scales.
Lyapunov inequalities for time scales.
Maximal regular boundary value problems in Banach-valued weighted space.
Pachpatte inequalities on time scales.
Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations.
On the asymptotic integration of nonlinear dynamic equations.
Opial inequalities on time scales
We present a version of Opial's inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.
Subexponential Solutions of Linear Volterra Difference Equations
We study the asymptotic behavior of the solutions of a scalar convolution sum-difference equation. The rate of convergence of the solution is found by determining the asymptotic behavior of the solution of the transient renewal equation.
Controllability and observability of time-invariant linear dynamic systems
In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.
Oscillation of third-order delay difference equations with negative damping term
The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results.
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