IJPAM: Volume 63, No. 4 (2010)

STABILITY OF THE NULL SOLUTION OF THE EQUATION
$\dot{x}(t)=-a(t)x(t)+b(t)x([t])$

Suzinei A.S. Marconato$^1$, Maria A. Bená$^2$
$^1$Department of Mathematics
Universidade Estadual Paulista
``Jülio de Mesquita Filho" - UNESP
CP 178, Rio Claro, 13500-230, SP, BRAZIL
e-mail: [email protected]
$^2$Department of Physics and Mathematics
Universidade Estadual Paulista
``Jülio de Mesquita Filho" - UNESP
Ribeirão Preto, 14040-901, SP, BRAZIL
e-mail: [email protected]


Abstract.The asymptotic stability of the null solution of the equation $\dot{x}(t)=-a(t)x(t)+b(t)x([t])$ with argument $[t]$, where $[t]$ designates the greatest integer function, is studied by means of dichotomic maps.

Received: August 2, 2010

AMS Subject Classification: 34K20, 39A11, 39A12

Key Words and Phrases: piecewise constant argument, stability, dichotomic maps

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 4