On some delay nonlinear integral inequalities in two independent variables

Some Nonlinear Integral Inequalities in Two Independent Variables

It is well known that the integral inequalities involving functions of one and more than one independent variables which provide explicit bounds on unknown functions play a fundamental role in the development of the theory of differential equations. In the past few years, a number of integral inequalities had been established by many scholars, which are motivated by certain applications. For de...

Nonlinear Integral Inequalities in Two Independent Variables on Time Scales

Some New Delay Integral Inequalities in Two Independent Variables on Time Scales

Some new Gronwall-Bellman type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete anal...

Some Retarded Nonlinear Integral Inequalities in Two Variables and Applications

In this paper, some retarded nonlinear integral inequalities in two variables with more than one distinct nonlinear term are established. Our results are also applied to show the boundedness of the solutions of certain partial differential equations.

Generalized 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...