Vector Lyapunov functions for practical stability of nonlinear impulsive functional differential equations

AbstractThis paper studies the practical stability of the solutions of nonlinear impulsive functional differential equations. The obtained results are based on the method of vector Lyapunov functions and on differential inequalities for piecewise continuous functions. Examples are given to illustrate our results

Stability criteria for impulsive Kolmogorov-type systems of nonautonomous differential equations

In this paper we consider a class of impulsive Kolmogorov- type systems. The problems of uniform stability and uniform asymptotic stability of the solutions are studied. We establish stability criteria by employing piecewise continuous Lyapunov functions. Examples are given to demonstrate the effectiveness of the obtained results. We show, also, that the role of impulses in changing the behavior of impulsive models is very important

Eventual stability and eventual boundedness for impulsive differential equations with “supremum”

Eventual stability and eventual boundedness for nonlinear impulsive differential equations with supremums are studied. The impulses take place at fixed moments of time. Piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed

Second Method of Lyapunov and Existence of Integral Manifolds for Impulsive Differential-Difference Equations

AbstractBy means of piecewise continuous functions which are analogues of Lyapunov's functions, sufficient conditions are obtained for the existence of integral manifolds for impulsive differential-difference equations with variable impulsive perturbations

Integral estimates of the solutions of fractional-like equations of perturbed motion

In this paper, the results of the analysis of nonlinear systems with fractional-like derivatives of the state vector are presented. Using the method of integral inequalities, some estimates of the solutions are obtained, and criteria for Heyers–Ulam–Rassias stability of a fractional-like scalar equation are established