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