Nonlinear integral inequalities involving maxima of unknown scalar functions. (English) Zbl 1217.26045

Henderson, Johnny; Hristova, Snezhana

Math. Comput. Modelling 53, No. 5-6, 871-882 (2011).

Summary: Some new nonlinear integral inequalities that involve the maximum of the unknown scalar function of one variable are solved. The inequalities considered are generalizations of a classical nonlinear integral inequality of Bihari. The importance of these integral inequalities is defined by their wide applications in qualitative investigations of differential equations with “maxima”, which is illustrated by some direct applications.

MSC:

26D15

Inequalities for sums, series and integrals

Keywords:

integral inequalities; maxima; scalar functions of one variable; differential equations with “maxima”

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