Integral inequalities of Bihari-type and applications. (English) Zbl 0717.45004

Pinto, Manuel

Funkc. Ekvacioj, Ser. Int. 33, No. 3, 387-403 (1990).

The author proves some integral inequalities with several nonlinear terms. Some of the inequalities are used to study the asymptotic behavior of the solutions of nth order differential equations. Examples are also given to illustrate the hypotheses of some of the results.
For the entire collection of such inequalities see the recent monograph by D. S. Mitrinović and J. E. Pecarić [Differential and integral inequalities, Naucna Knjiga Belgrade (1988; MR 90c.26055)].

Reviewer: B.G.Pachpatte

MSC:

45G10	Other nonlinear integral equations
26D15	Inequalities for sums, series and integrals
34E05	Asymptotic expansions of solutions to ordinary differential equations

Keywords:

integral inequalities of Bihari-type; Gronwall-Bellman inequality; Bihari’s inequality; nonlinear; asymptotic behavior