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This article investigates the relationship between an unperturbed integrodifferential system and a perturbed integrodifferential system that have different initial positions and an initial time difference (ITD). Variation of parameter techniques are employed to obtain integral formulae and to define Lyapunov-like functions. [ABSTRACT FROM AUTHOR]

In this paper, we study a differential hemivariational inequality (DHVI, for short) in the framework of reflexive Banach spaces. Our aim is three fold. The first one is to investigate the existence and the uniqueness of mild solution, by applying a general fixed-point principle. The second one is to study its exponential stability, by employing the formula for the variation of parameters and inequality techniques. Finally, the third aim is to illustrate an application of our abstract results in the study of an initial and boundary value problem which describes the contact of an elastic rod with an obstacle. [ABSTRACT FROM AUTHOR]

In this article we consider the difference equation with a smoothness condition on f with respect to y . We study the dependence of solutions of ( A ) on initial data and then obtain a discrete analog of Alekseev's variation of parameters formula. In addition, we develop a Variational Lyapunov Method (VLM) and use it to study the stability properties of difference equations. [ABSTRACT FROM AUTHOR]