Some nonlinear dynamic inequalities on time scales

Some Nonlinear Dynamic Inequalities on Time Scales

Our aim in this paper is to establish some explicit bounds of solutions of a certain class of nonlinear dynamic inequalities on a time scale T which is unbounded above. Also, we establish some sufficient conditions for global existence and an estimate of the rate of decay of the solutions. These on the one hand generalizes and on the other hand furnish a handy tool for the study of qualitative ...

Some Nonlinear Dynamic Inequalities on Time Scales and Applications

Some nonlinear dynamic inequalities on a time scale T are formulated in this paper. Some sufficient conditions for global existence and an estimate of the rate of decay of solutions are obtained. The results not only unify the results of differential and difference inequalities but can be applied on different types of time scales. These inequalities are of interest in a study of continuous and ...

Some nonlinear dynamic integral inequalities on time scales

On Some Nonlinear Integral Inequalities on Time Scales

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.

Research Article Some Nonlinear Integral Inequalities on Time Scales

The theory of time scales was introduced by Hilger [1] in his Ph.D. thesis in 1988 in order to unify continuous and discrete analysis. Recently, many authors have extended some fundamental integral inequalities used in the theory of differential and integral equations on time scales. For example, we refer the reader to the literatures [2–8] and the references cited therein. In this paper, we in...