Title: Razumikhin method and cone valued Lyapunov functions for impulsive differential equations with 'supremum'

Authors: Snezhana G. Hristova

Addresses: Department of Applied Mathematics and Modeling, Plovdiv University, 4000 Plovdiv, Bulgaria

Abstract: Stability of nonlinear impulsive differential equations with |supremum| is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

Keywords: stability in two measures; cone-valued Lyapunov functions; impulsive differential equations; supremum; piecewise continuous Lyapunov functions; Razumikhin method; nonlinear differential equations.

DOI: 10.1504/IJDSDE.2009.031103

International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.3/4, pp.223 - 236

Published online: 20 Jan 2010 *

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