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Open Access Research Article

On Some Generalizations Bellman-Bihari Result for Integro-Functional Inequalities for Discontinuous Functions and Their Applications

Angela Gallo1* and AnnaMaria Piccirillo2

Author Affiliations

1 Department of Mathematics and Applications, "R.Caccioppoli" University of Naples "Federico II", Claudio street 21, 80125 Naples, Italy

2 Department of Civil Engineering, Second University of Naples, Roma, street 21, 81100 Caserta, Italy

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Boundary Value Problems 2009, 2009:808124  doi:10.1155/2009/808124

Published: 29 June 2009

Abstract

We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions (integro-sum inequalities; impulse integral inequalities). Some applications of the results are included: conditions of boundedness (uniformly), stability by Lyapunov (uniformly), practical stability by Chetaev (uniformly) for the solutions of impulsive differential and integro-differential systems of ordinary differential equations.