Some Pachpatte type inequalities on time scales

AbstractIn this paper, using the comparison theorem, we investigate some Pachpatte type integral inequalities on time scales, which provide explicit bounds on unknown functions. Our results extend some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Some applications of the main results are given in the end of this paper

A new Pachpatte type dynamic inequality on time scales

In this paper, using the comparison theorem, we investigate a new Pachpatte type dynamic inequality on time scales, which provides explicit bounds on unknown functions. Our result unifies and extends a continuous inequality and its corresponding discrete analogues

On Stability and Stabilization of Perturbed Time Scale Systems with Gronwall Inequalities

In the paper, new nonlinear time scale integral inequalities are given. By means of the explicit integral bounds, we derive suffcient conditions for the uniform asymptotic stability of perturbed systems on time scales. In the sequel, basing on Lyapunov's direct method, we develop the required type of stability.В статье представлены новые нелинейные интегральные неравенства на временной шкале. С помощью явных интегральных оценок получены достаточные условия для равномерной асимптотической устойчивости возмущенных систем на временных шкалах. Далее, основываясь на прямом методе Ляпунова, разработан нужный тип стабильности