Integral inequalities for retarded Volterra equations. (English) Zbl 1103.26018

Summary: Integral inequalities are very useful in the qualitative analysis of differential and integral equations. Starting with [the author, J. Math. Anal. Appl. 252, No. 1, 389–401 (2000; Zbl 0974.26007)], several recent investigations [see the author, ibid. 285, No. 2, 436–443 (2003; Zbl 1040.26007); B. G. Pachpatte, ibid. 267, No. 1, 48–61 (2002; Zbl 0996.26008); JIPAM, J. Inequal. Pure Appl. Math. 3, No. 2, Paper No. 18 (2002; Zbl 0994.26017); ibid. 5, No. 1, Paper No. 19 (2004; Zbl 1068.26011) and ibid. 5, No. 3, Paper No. 80 (2004; Zbl 1068.26020)] were devoted to retarded integral inequalities.
In this paper we consider the case of retarded Volterra integral equations. We establish bounds on the solutions and, by means of examples, we show the usefulness of our results in investigating the asymptotic behaviour of the solutions.


26D15 Inequalities for sums, series and integrals
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