Paper's Title:

Some New Nonlinear Integro-Differential Inequalities of Gronwall-Bellman-Pachpatte Type

Author(s):

A. ABDELDAIM

Department of Mathematics and Computer Sciences,
Faculty of Science,
Port Said University, Port Said,
EGYPT.

Department of Mathematics,
Faculty of Science and Humanities,
Shaqra University, Dawadmi,
SAUDI ARABIA.

E-mail: ahassen@su.edu.sa
URL: http://faculty.ksu.edu.sa/DRABDELDAIM/Pages/Home.aspx

Abstract:

In this paper we establish some new nonlinear integro-differential inequalities of Gronwall-Bellman-Pachpatte type for function of one independent variable. The purpose of this paper is to extend certain results which proved by Pachpatte in [On some fundamental integrodifferential and integral inequalities, An. Sti. Univ. Al. I. Cuza, Iasi, Vol.23 (1977), 77-86]. The inequalities obtained here can be used in the theory of some new classes of nonlinear integro-differential equations. Some applications are also given to illustrate the usefulness of our results.

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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