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

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
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[1] Bainov, D.D.; Simeonov, P.S., Integral inequalities and applications, (1989), Kluwer · Zbl 0672.26009
[2] Cho, Y.; Kim, Y.-H.; Pecaric, J., New gronwall – ou – iang type integral inequalities and their applications, Anziam j., 50, 1, 111-127, (2008) · Zbl 1171.26323
[3] Ferreira Rui, A.C.; Torres Delfim, F.M., Generalized retarded integral inequalities, Appl. math. lett., 22, 876-881, (2009) · Zbl 1171.26328
[4] Pachpatte, B.G., Explicit bounds on certain integral inequalities, J. math. anal. appl., 267, 48-61, (2002) · Zbl 0996.26008
[5] Angelov, V.G.; Bainov, D.D., On the functional differential equations with maximums, Appl. anal., 16, 187-194, (1983) · Zbl 0524.34069
[6] Hristova, S.G.; Roberts, L.F., Boundedness of the solutions of differential equations with maxima, Int. J. appl. math., 4, 2, 231-240, (2000) · Zbl 1172.34336
[7] Otrocol, D.; Rus Ioan, A., Functional-differential equations with maxima via weakly Picard operators theory, Bull. math. soc. sci. math. roumanie (NS), 51, 99, 253-261, (2008), no. 3 · Zbl 1194.34121
[8] E.P. Popov, Automatic Regulation and Control, Moscow, 1966 (in Russian).
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