Practical Stability of Impulsive Differential Equations with “Supremum” by Integral Inequalities

Snezhana Hristova, Kremena Stefanova

Abstract

The paper deals with some stability properties of the solutions of impulsive differential equations with “supremum”. Initially several integro-summation inequalities for piecewise continuous functions are solved. The main characteristic of the considered inequalities is the presence of the supremum of the unknown function over a past time interval. These inequalities are generalizations of Bihari’s integral inequality. They are base of studying the practical stability as well as the uniform practical stability of the solutions of nonlinear impulsive differential equations with “supremum”.

Keywords

Integral Inequality, Supremum, Practical Stability, Impulses

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