Generalized Gronwall-Bellman-type delay dynamic inequalities on time scales and their applications

详细信息    查看全文

• 作者：Qinghua Feng ; Bin Zheng ; ^{zhengbin2601@126.com}
• 关键词：Gronwall&ndash ; Bellman-type inequality ; Time scales ; Delay ; Dynamic equation
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 出版时间：1 April, 2012
• 年：2012
• 卷：218
• 期：15
• 页码：7880-7892
• 全文大小：272 K

文摘

In this paper, we establish some new Gronwall-Bellman-type delay dynamic inequalities on time scales, which can be used as a handy tool in the investigation of qualitative as well as quantitative analysis of solutions of delay dynamic equations on time scales. Our results generalize the main results of Ou-Iang [L. Ou-Iang, The boundedness of solutions of linear differential equations y?#xA0;+ A(t)y = 0, Shuxue Jinzhan 3 (1957) 409-415], Jiang [F.C. Jiang, F.W. Meng, Explicit bounds on some new nonlinear integral inequality with delay, J. Comput. Appl. Math. 205 (2007) 479-486.] and Yuan [Z.L. Yuan, X.W. Yuan, F.W. Meng, Some new delay integral inequalities and their applications, Appl. Math. Comput. 208 (2009) 231-237].