On Some Generalizations Bellman-Bihari Result for Integro-Functional Inequalities for Discontinuous Functions and Their Applications
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
Boundary Value Problems 2009, 2009:808124 doi:10.1155/2009/808124Published: 29 June 2009
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.