Research Article Nonlinear Integral Inequalities in Two Independent Variables and Their Applications
نویسندگان
چکیده
The integral inequalities play a fundamental role in the study of existence, uniqueness, boundedness, stability, invariant manifolds, and other qualitative properties of solutions of the theory of differential and integral equations. There are a lot of papers investigating them such as [1–8]. In particular, Pachpatte [2] discovered some new integral inequalities involving functions of two variables. These inequalities are applied to study the boundedness and uniqueness of the solutions of the following terminal value problem for the hyperbolic partial differential equation (1.1) with conditions (1.2):
منابع مشابه
Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two variables and their applications
In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.
متن کاملA generalization of retarded integral inequalities in two independent variables and their applications
The object of this paper is to establish some nonlinear retarded integral inequalities in two independent variables which can be used as handy tools in the theory of partial differential and integral equations with time delays.
متن کاملGeneralized Delay Integral Inequalities In Two Independent Variables On Time Scales
Abstract: In this paper, we discuss some new Gronwall-Bellman type delay integral inequalities in two independent variables on time scales, which contain arbitrary nonlinear items on unknown functions outside the integrals as well as inside the integrals. The inequalities established have different forms compared with the existing GronwallBellman type inequalities so far in the literature. As a...
متن کاملOn Certain New Nonlinear Retarded Integral Inequalities for Functions in Two Variables and Their Applications
Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.
متن کاملSome new results using Hadamard fractional integral
Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse ...
متن کامل