IJPAM: Volume 70, No. 1 (2011)

CONTINUOUS DEPENDENCE AND STABILITY OF
SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS
ON THE INITIAL CONDITIONS AND IMPULSIVE MOMENTS

A.B. Dishliev$^1$, K.G. Dishlieva$^2$
$^1$Department of Mathematics
University of Chemical Technology and Metallurgy
8, Kliment Ohridsky, Sofia 1756, BULGARIA
e-mail: dishliev@uctm.edu
$^2$Faculty of Applied Mathematics and Informatics
Technical University of Sofia
Sofia, BULGARIA
email: kgd@tu-sofia.bg


Abstract. Basic research object in the present paper are non-linear impulsive systems of differential equations with fixed moments of impulsive effects. For such type of equations are introduced the concepts continuous dependence and stability on the initial data and impulsive moments. Sufficient conditions are found under which the solutions have these properties. The results are applied to a mathematical model of pharmacokinetics.

Received: January 28, 2011

AMS Subject Classification: 34A37, 92C50

Key Words and Phrases: impulsive systems, differential equations, continuous dependence, stability, initial conditions, impulsive moments

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 1