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Explicit bounds of unknown function of some new weakly singular retarded integral inequalities for discontinuous functions and their applications

The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of singular differential equations...

Some new generalized retarded nonlinear integral inequalities with iterated integrals and their applications

Some new generalized retarded nonlinear integral inequalities with iterated integrals are discussed and upper bound estimations of unknown functions are given by analysis technique. These estimations can be used as tools in the study of differential-integral equations with the initial conditions.MSC: 26D10, 26D15, 26D20, 34A12, 34A40.

A class of retarded nonlinear integral inequalities and its application in nonlinear differential-integral equation

In this paper, we discuss a class of retarded nonlinear integral inequalities and give an upper bound estimation of an unknown function by the integral inequality technique. This estimation can be used as a tool in the study of differential-integral equations with the initial conditions.MSC: 26D10, 26D15, 26D20, 34A12, 34A40.

Some retarded nonlinear integral inequalities and their applications in retarded differential equations

In this article, we discuss some generalized retarded nonlinear integral inequalities, which not only include nonlinear compound function of unknown function but also include retard items, and give upper bound estimation of the unknown function by integral inequality technique. This estimation can be used as tool in the study of differential equations with the initial conditions...

Generalized retarded nonlinear integral inequalities involving iterated integrals and an application

In this work, some new generalized retarded nonlinear integral inequalities, which include nonlinear composite functions of unknown functions between iterated integrals, are discussed. By adopting novel analysis techniques, the upper bounds of the embedded unknown functions are estimated explicitly. The derived results can be applied in the study of differential-integral...

Some generalized nonlinear retarded integral inequalities with applications

In this article we discuss some new generalized nonlinear Gronwall-Bellman-Type integral inequalities with two variables, which include a non-constant term outside the integrals. We use our result to deal with the estimate on the solutions of partial differential equations with the initial and boundary conditions. Mathematics Subject Classification 2000: 26D10; 26D15; 26D20; 34A40.

A New Nonlinear Retarded Integral Inequality and Its Application

The main objective of this paper is to establish a new retarded nonlinear integral inequality with two variables, which provide explicit bound on unknown function. This inequality given here can be used as tool in the study of integral equations.

Nonlinear Retarded Integral Inequalities with Two Variables and Applications

We consider some new nonlinear retarded integral inequalities with two variables, which extend the results in the work of W.-S. Wang (2007), and the one in the work of Y.-H. kim (2009). These inequalities include not only a nonconstant term outside the integrals but also more than one distinct nonlinear integrals without assumption of monotonicity. Finally, we give some...

On a Generalized Retarded Integral Inequality with Two Variables

This paper improves Pachpatte's results on linear integral inequalities with two variables, and gives an estimation for a general form of nonlinear integral inequality with two variables. This paper does not require monotonicity of known functions. The result of this paper can be applied to discuss on boundedness and uniqueness for a integrodifferential equation.