About some new generalizations of Bellman–Bihari results for integro-functional inequalities with discontinuous functions and applications Original Research Article

In this article we present some new nonlinear Bellman–Bihari type integral inequalities 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.