In this paper we analyze asymptotic stability of the dynamical system x˙ = f(x) defined by a C1 function f : D Rn where D Rn + is an open set. We obtain a criterion of stability for the equilibrium solution ¯x D ...

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic ...

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic ...

The paper deals with the analysis of the behavior of a nonsmooth three-dimensional vector field around a typal singularity. We focus on a class of generic one-parameter families (Formula presented.) of Filippov systems and ...

In this paper we study topological properties of Lyapunov stable sets for semigroup actions on Tychonoff spaces. We show that the stability and the asymptotical stability of a compact set is characterized by the stability ...

We study the existence and the asymptotic behavior of the solution of an abstract viscoelastic system submitted to non-local initial data. u(tt )+ Au - integral(t)(0) g(t - s)Bu(s)ds = 0 u(0) = xi(u) in V, u(t) (0) = eta(u) ...

Global almost sure asymptotic stability of solutions of some nonlinear stochastic difference equations with cubic-type main part in their drift and diffusive part driven by square-integrable martingale differences is proven ...