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Some retarded nonlinear integral inequalities and their applications in retarded differential equations. (English) Zbl 1279.26036

Summary: We discuss some generalized retarded nonlinear integral inequalities, which does not only include nonlinear compound function of an unknown function but also include retarded items, and give upper bound estimation of the unknown function by integral inequality technique. This estimation can be used as tool in the study of differential equations with the initial conditions.

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
26D20 Other analytical inequalities
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A40 Differential inequalities involving functions of a single real variable
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