Stability of differential equations with piecewise constant argument via discrete equations

Lyapunov stability for a class of differential equation with piecewise constant argument (EPCA) is considered by means of the stability of a discrete equation. Applications to some nonlinear autonomous equations are given improving some linear known cases.

Measure Functional Differential Equations in the Space of Functions of Bounded Variation

We establish general conditions for the unique solvability of nonlinear measure functional differential equations in terms of properties of suitable linear majorants.

Stability of multistep second derivative methods for integro-differential equations

The stability of multistep second derivative methods for integro-differential equations is examined through a test equation which allows for the construction of the associated characteristic polynomial and its region of stability (roots in the unit circle) at a proper parameter space. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Stability of neutral functional differential equations in terms of measures

In this paper we investigate the relationships between different concepts of stability in measure for the solutions of an autonomous or periodic neutral functional differential equation.

On retarded differential equations with impulses

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bifurcation of limit cycles from an n-dimensional linear center inside a class of piecewise linear differential systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Implicit differential equations with impasse singularities and singular perturbation problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier B.V. All rights reserved.

Stability results for impulsive functional differential equations with infinite delay

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.

On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some results on stability of retarded functional differential equations using dichotomic map techniques

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 stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation x′(t) = -b(t)x(t - r) and of its nonlinear generalization x′(t) = b(t) f (x(t - r)) are established. © 1998 Kluwer Academic Publishers.