On some new integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions and their applications

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• 作者：Xiaohong Liu^a ; ^{342797283@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Lihong Zhang^b ; ^{zhanglih149@126.com" class="auth_mail" title="E-mail the corresponding author} ; Praveen Agarwal^c ; ^{goyal.praveen2011@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Guotao Wang^b ; ^{wgt2512@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Integral inequalities ; Discontinuous functions ; Gronwall&ndash ; Bellman&ndash ; Bihari type inequalities ; Impulsive differential systems
• 刊名：Indagationes Mathematicae
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：27
• 期：1
• 页码：1-10
• 全文大小：178 K

文摘

In this article, some new explicit bounds on solutions to a class of new nonlinear integral inequalities of Gronwall–Bellman–Bihari type with delay for discontinuous functions are established. These inequalities generalize and improve some former famous results about inequalities, and which provide an excellent tool to discuss the qualitative and quantitative properties for solutions to some nonlinear differential and integral equations. To illustrate our results, we present an example to show estimated solutions for an impulsive differential system.