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) + m m − n α (t ) 0 f (s)un(s)w u(s) + g(s)un(s) ds and um(t ) cm/(m−n) + m m − n α (t ) 0 f (s)un(s)w u(s) ds + m m −n t 0 g(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.  2004 Elsevier Inc. All rights reserved