Nonlinear integral inequality in two independent variables

Nonlinear Integral Inequalities in Two Independent Variables on Time Scales

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...

A Generalized Gronwall–bellman Type Delay Integral Inequality with Two Independent Variables on Time Scales

Using a technique of monotonization, this paper investigates a generalized GronwallBellman type delay integral inequality with two independent variables on time scales. The result not only unifies some continuous inequalities and their discrete analogues but also extends some known integral inequalities on time scales. An application to the estimation of solutions of delay dynamic integral equa...

Research Article Nonlinear Integral Inequalities in Two Independent Variables and Their Applications

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 varia...

Nonlinear Dynamic Integral Inequalities in two Independent Variables on Time Scale Pairs

We extend from the discrete case some nonlinear inequalities in two independent variables to a more general dynamic setting involving pairs of time scales. These inequalities provide explicit bounds on unknown functions, which can be useful in the study of qualitative properties of solutions of certain classes of dynamic equations on time scales. Several examples are provided. AMS subject class...