Nonlinear integral inequality with power and its application in delay integro-differential equations

被引：0
作者：
Yazhou Tian
Min Fan
机构：
[1] University of Jinan,School of Mathematical Sciences
[2] Qingdao University of Technology,undefined
来源：
Advances in Difference Equations | / 2020卷
关键词：
Nonlinear; Integral inequality; Power; Delay IDE; 26D10; 26D15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
New nonlinear integral inequalities (NII) are presented in this paper. Based on mathematical analysis technique, several estimation results are obtained, which not only complement the aforementioned results, but also generalize the inequalities to the more general nonlinearities. As an application, they can be employed to estimate the bound on the solutions of power integro-differential equations (IDE).
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[1]  
Gronwall T.H.(1919)Note on the derivatives with respect to a parameter of the solutions of a system of differential equations Ann. Math. 20 292-296
[2]  
Bihari I.(1956)A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations Acta Math. Acad. Sci. Hung. 7 71-94
[3]  
Tian Y.Z.(2015)Asymptotic behavior of switched delay systems with nonlinear disturbances Appl. Math. Comput. 268 522-533
[4]  
Cai Y.L.(2019)Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Gronwall–Bellman–Bihari’s type Appl. Math. Comput. 350 60-65
[5]  
Sun Y.G.(2007)Explicit bounds on some new nonlinear integral inequalities with delay J. Comput. Appl. Math. 205 479-486
[6]  
Zada A.(2011)Gronwall–Bellman type nonlinear delay integral inequalities on time scales J. Math. Anal. Appl. 382 772-784
[7]  
Ali W.(2014)Some new nonlinear Volterra–Fredholm type dynamic integral inequalities on time scales Appl. Math. Comput. 245 235-242
[8]  
Park C.(2017)A class of retarded Volterra–Fredholm type integral inequalities on time scales and their applications J. Inequal. Appl. 2017 802-814
[9]  
Jiang F.C.(2018)Some new integral inequalities with mixed nonlinearities for discontinuous functions Adv. Differ. Equ. 2018 375-380
[10]  
Meng F.W.(2006)Some new dynamic inequalities on time scales J. Math. Anal. Appl. 319 239-248
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