Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay

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• 作者：Lianzhong Li^a ; ^b ; ^{llz3497@163.com} ; Fanwei Meng^b ; ^{fwmeng@qfnu.edu.cn} ; Peijun Ju^a
• 关键词：Integral inequality ; Integral equation ; Differential equation ; Integro-differential equation ; Uniform stability
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 May 2011
• 年：2011
• 卷：377
• 期：2
• 页码：853-862
• 全文大小：165 K

文摘

In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of our's. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integro-differential equations with time delay.