Discrete Nonlinear Inequalities Research Articles

On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications

Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.

Some Discrete Nonlinear Inequalities in Two Variables

In this paper, some discrete nonlinear inequalities in two variables are established. The inequalities given here can be used as tools in the qualitative theory of certain finite difference equations.

Some Discrete Nonlinear Inequalities and Applications to Difference Equations

In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.

Discrete non-linear inequalities and applications to boundary value problems

In this paper, we generalize some existing discrete Gronwall–Bellman–Ou-Iang-type inequalities to more general situations. These are in turn applied to study the boundedness, uniqueness, and continuous dependence of solutions of certain discrete boundary value problem for difference equations.

Some Discrete Nonlinear Inequalities and Applications to Boundary Value Problems for Difference Equations

In this paper, we establish some new discrete Gronwall–Bellman–Ou-Iang type inequalities over 2-dimensional lattices. These, on one hand, generalize some existing results in the literature and on the other hand, provide a handy tool for the study of qualitative properties of solutions of difference equations. We illustrate this by applying these new results to certain boundary value problem for difference equations.