On stability of differential equations with piecewise constant argument using dichotomic maps

Marconato, S. A S [UNESP]Bená, M. A.Spezamiglio, A. [UNESP]2014-05-272014-05-272011-02-08Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, v. 18, n. 2, p. 257-268, 2011.1201-3390http://hdl.handle.net/11449/72308This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.257-268engDichotomic mapsLiapunov stabilityPiecewise constant argumentOn stability of differential equations with piecewise constant argument using dichotomic mapsArtigoAcesso restrito2-s2.0-79551581258