Explicit bounds of unknown function of some new weakly singular retarded integral inequalities for discontinuous functions and their applications.

The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of singular differential equations and singular impulsive equations.