On some generalizations of nonlinear dynamic inequalities on time scales and their applications

Abstract

In this article, by using Young's inequality, we prove some new nonlinear dynamic inequalities of Gronwall-Bellman-Pachpatte type on time scales. These inequalities give us the integral and discrete version, and also extend some known dynamic inequalities in certain papers. We can also say, the inequalities proved in this paper can be used as handy tools in the study of qualitative properties of some dynamic equations on time scales. Some examples are introduced to demonstrate the applications of these inequalities.