On retarded integral inequalities and their applications

The main results of [J. Math. Anal. Appl. 285 (2003) 436-443] are here generalized to the following retarded integral inequalities: um(t)⩽cm/(m−n)+mm−n∫0α(t)[f(s)un(s)w(u(s))+g(s)un(s)]ds and um(t)⩽cm/(m−n)+mm−n∫0α(t)f(s)un(s)w(u(s))ds+mm−n∫0tg(s)un(s)w(u(s))ds, where m>n>0 are constants and t∈R+=[0,∞). The results given here can be applied to the global existence of solutions to differential equations with time delay.