Abstract
AbstractThe main objective of the present article is to prove some new delay nonlinear dynamic inequalities of Gronwall–Bellman–Pachpatte type on time scales. We introduce very important generalized results with the help of Leibniz integral rule on time scales. For some specific time scales, we further show some relevant inequalities as special cases: integral inequalities and discrete inequalities. Our results can be used as handy tools for the study of qualitative and quantitative properties of solutions of dynamic equations on time scales. Some examples are provided to demonstrate the applications of the results.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference45 articles.
1. Gronwall, T.H.: Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. Math. (2) 20(4), 292–296 (1919)
2. Bellman, R.: The stability of solutions of linear differential equations. Duke Math. J. 10, 643–647 (1943)
3. Bellman, R.: Asymptotic series for the solutions of linear differential-difference equations. Rend. Circ. Mat. Palermo 7, 1–9 (1958)
4. Pachpatte, B.G.: On some fundamental integral inequalities and their discrete analogues. J. Inequal. Pure Appl. Math. 2(2), 1–13 (2001)
5. Pachpatte, B.G.: On some new inequalities related to a certain inequality arising in the theory of differential equations. J. Math. Anal. Appl. 251(2), 736–751 (2000)
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