Georgian Mathematical Journal 13 (2006), No. 2, 229--238
Copyright Heldermann Verlag 2006
A Generalization of Bihari's Lemma for Discontinuous Functions and Its Application to the Stability Problem of Differential Equations with Impulse Disturbance
Sergiy Borysenko
Dept. of Differential Equations, National Technical University, Peremogy Prosp. 37, 03056 Kyiv, Ukraine
borys@mbox.com.ua
Giovanni Matarazzo
Dept. of Engineering, Informatics and Applied Mathematics, University of Salerno, Ponte Don Melillo, 84084 Fisciano, Italy
matarazz@diima.unisa.it
Massimo Pecoraro
Dept. of Engineering, Informatics and Applied Mathematics, University of Salerno, Ponte Don Melillo, 84084 Fisciano, Italy
This paper presents a generalization of nonlinear integral inequalities of the Gronwall-Bellman-Bihari type for discontinuous functions and its application to the investigation of the practical stability of solutions of systems of integro-differential equations with impulse perturbations at fixed moments of time.
Keywords: Differential equations with impulse perturbations, integral inequalities.
MSC: 34B15
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