Boundary Value Problems
Volume 2009 (2009), Article ID 808124, 14 pages
doi:10.1155/2009/808124
Research Article

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

Angela Gallo1 and Anna Maria Piccirillo2

1Department of Mathematics and Applications, “R.Caccioppoli” University of Naples “Federico II”, Claudio street 21, 80125 Naples, Italy
2Department of Civil Engineering, Second University of Naples, Roma, street 21, 81100 Caserta, Italy

Received 22 December 2008; Revised 21 April 2009; Accepted 28 May 2009

Academic Editor: Juan J. Nieto

Copyright © 2009 Angela Gallo and Anna Maria Piccirillo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.