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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (2): 261-268.doi: 10.3969/j.issn.1005-3085.2015.02.010

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带迭代积分的滞后型非线性积分不等式及其应用

张  倩,   薛书文,   郑召文   

  1. 曲阜师范大学数学科学学院，曲阜  273165
  • 收稿日期:2013-10-09 接受日期:2014-12-25 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    国家自然科学基金 (11271225; 11171178)；国家级大学生创新训练计划项目 (201310446008).

Retarded Nonlinear Integral Inequalities with Iterative Integral and Their Applications

ZHANG Qian,   XUE Shu-wen,   ZHENG Zhao-wen   

  1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165
  • Received:2013-10-09 Accepted:2014-12-25 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The National Natural Science Foundation of China (11271225; 11171178;); the Scientific Research Training Project for Talent Students (201310446008).

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摘要： Growall-Bellman型积分不等式在微分方程解的稳定性，有界性，渐近性与解的其它定性与定量性质的分析方面具有十分重要的作用．本文研究了几类带有迭代积分的滞后型非线性积分不等式．利用分析的方法和微分不等式的一般理论，给出未知函数的上界估计．最后将本文结果应用到一类非线性微分--积分方程中，得到所有解的一个上界估计，从而为微分方程解的估计、动力系统及控制工程理论的研究提供了理论依据．

关键词: 积分不等式, 迭代积分, 滞后, 非线性积分--微分方程, 估计

Abstract:

Growall-Bellman inequality is one of the most important inequalities investigating the qualitative and quantitative properties of solutions for differential equations such as stability, boundedness, asymptotic property. In this paper, some new generalized retarded nonlinear integral inequalities are discussed, and upper bound estimations of unknown functions are given by applying analysis technique and classical inequalities theories. These estimations can be employed ied to the certain nonlinear differential-integral equations. Finally, the upper bound of all solutions is given, which is the theoretic\, basis for the estimation of solutions, dynamical systems and control system.

Key words: integral inequality, iterative integral, delay, nonlinear differential-integral equation, estimation

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