Department of Mathematics, University of Constantine 1 Brothers Mentouri,
BP, 325, Ain El Bey Street, 25017,
Algeria.
E-mail: ammar_boudeliou@umc.edu.dz

Abstract:

In this paper, we investigate a certain class of nonlinear Gronwall-Bellman type integral inequalities with power in more general cases involving retarded term and more general nonlinearities. Our results generalize some known integral inequalities and other results obtained very recently. The inequalities given here can be used to estimate the bound on the solutions of retarded integral equation of Volterra type and integro-differential equations (IDE) with power. Two examples are given to show the validity of our established theorems.

Paper's Title:

Estimation for Bounded Solutions of Some Nonlinear Integral Inequalities with Delay in Several Variables

Author(s):

Smakdji Mohamed Elhadi, Denche Mouhamed and Khellaf Hassane

Department of Mathematics
University of Frères Mentouri
PO Box 25000, Ain Elbay,
Constantine,
Algeria.
E-mail: khellafhassane@umc.edu.dz

Abstract:

In this paper, some new nonlinear retarded integral inequalities of Gronwall-Bellman type for functions of two and n-independents variables are investigated. The derived results can be applied in the study of differential-integral equations with time delay. An example is given to illustrate the application of our results.

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