[1]李自尊.含多个非线性项的Gronwall-Bellman 型非连续函数积分不等式的推广[J].四川师范大学学报(自然科学版),2018,(03):305-310.[doi:10.3969/j.issn.1001-8395.2018.03.004]
 LI Zizun.Generalization of Gronwall-Bellman Type Integral Inequality of Discontinuous Functions with Multiple Nonlinear Terms[J].Journal of SichuanNormal University,2018,(03):305-310.[doi:10.3969/j.issn.1001-8395.2018.03.004]
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含多个非线性项的Gronwall-Bellman 型非连续函数积分不等式的推广()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年03期
页码:
305-310
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
Generalization of Gronwall-Bellman Type Integral Inequality of Discontinuous Functions with Multiple Nonlinear Terms
文章编号:
1001-8395(2018)03-0305-06
作者:
李自尊12
1.四川大学 数学学院, 四川 成都 610064;
2.百色学院 数学与统计学院, 广西 百色 533000
Author(s):
LI Zizun12
1.School of Mathematics, Sichuan University, Chengdu 610064, Sichuan;
2.School of Mathematics and Statistics, Baise University, Baise 533000, Guangxi
关键词:
非连续函数积分不等式 未知函数估计 脉冲微分系统
Keywords:
Integral inequality for discontinuous function estimation of unknown function impulsive differential system
分类号:
O178
DOI:
10.3969/j.issn.1001-8395.2018.03.004
文献标志码:
A
摘要:
研究了含有未知函数的多个非线性项的非连续函数积分不等式,对每一个区间的估计,在未把不等式右边第一项放大为常数,而是保持为函数的情况下,利用分析技巧给出了未知函数的上界估计.利用此结果估计了脉冲微分方程解的上界.
Abstract:
In this paper, I give the upper bounds estimation of the unknown function contained in multiple nonlinear terms of integral inequality for discontinuous functions. I estimate each interval without enlarging the inequality of the first term on the right side to a constant, and remaining the case for a function. The result is used to estimate the upper bounds of impulsive differential equations.

参考文献/References:

[1] AGARWAL R P, DENG S F, ZHANG W N. Generalization of a retarded Gronwall-like inequality and its applications[J]. Appl Math Comput,2005,165(3):599-612.
[2] WANG W S. A generalized retarded Gronwall-like inequality in two variables and applications to BVP[J]. Appl Math Comput,2007,191(1):144-154.
[3] 王五生,李自尊. 一类新的非线性时滞积分不等式及其应用[J]. 四川师范大学学报(自然科学版),2012,35(2):180-183.
[4] IOVANE G. Some new integral inequalities of Bellman-Bihari type with delay for discontinuous functions[J]. Nonlinear Anal,2007,66(2):498-508.
[5] 严勇. 一类带脉冲项的Gronwall-Bellman型积分不等式的推广及应用[J]. 四川师范大学学报(自然科学版),2013,36(4):603-609.
[6] 米玉珍,钟吉玉. 非连续函数的Bellman-Bihari 型积分不等式的推广[J]. 四川大学学报(自然科学版),2015,52(1):33-38.
[7] BORYSENKO S D. About asymptotical stability on linear approximation of the systems with impulse influence[J]. Ukrain Mat Zh,1983,35(2):144-150.
[8] BORYSENKO S D, CIARLETTA M, IOVANE G. Integro-sum inequalities and motion stability of systems with impulse perturbations[J]. Nonlinear Anal,2005,62(3):417-428.
[9] GALLO A, PICCIRILLO A M. About new analogies of Gronwall-Bellman-Bihari type inequalities for discontinuous functions and estimated solutions for impulsive differential systems[J]. Nonlinear Anal,2007,67(5):1550-1559.
[10] GALLO A, PICCIRILLO A M. About some new generalizations of Bellman-Bihari results for integro-functional inequalities with discontinuous functions and applications[J]. Nonlinear Anal,2009,71(12):e2276-e2287.
[11] 李自尊. 脉冲积分不等式未知函数的估计[J]. 四川师范大学学报(自然科学版),2013,36(2):258-262.
[12] 柳长青,李自尊. 一类新的非连续函数积分不等式及其应用[J]. 理论数学,2013,3(1):4-8.
[13] 孟东沅. 一类新型不连续函数的积分不等式及应用[J]. 数学的实践与认识,2009,39(2):161-166.
[14] MI Y Z, DENG S F, LI X P. Nonlinear integral inequalities with delay for discontinuous functions and their applications[J]. J Inequal Appl,2013,2013:1-11.
[15] MITROPOLSKI Y A, IOVANE G, BORYSENKO S D. About a generalization of Bellman-Bihari type inequalities for discontinuous functions and their applications[J]. Nonlinear Anal,2007,66(10):2140-2165.
[16] WANG W S, LI Z Z. A new class of impulsive integral inequalities and its application[C]//2011 International Conference on Multimedia Technology,2011,3(1):1897-1899.

相似文献/References:

[1]严勇.一类非线性Mate-Nevai型离散不等式及其应用[J].四川师范大学学报(自然科学版),2011,(05):677.
 YAN Yong.A Class of Nonlinear Discrete MateNevai Inequalities and Their Applications[J].Journal of SichuanNormal University,2011,(03):677.
[2]王五生.一类非连续函数积分不等式中未知函数的估计[J].四川师范大学学报(自然科学版),2011,(01):43.
 WANG Wu sheng.Estimation of Unknown Functions of a Class of Integral Inequalities for Discontinuous Functions[J].Journal of SichuanNormal University,2011,(03):43.

备注/Memo

备注/Memo:
收稿日期:2017-08-12 接受日期:2017-09-22
基金项目:国家自然科学基金(11561019)、广西自然科学基金(2013GXNSFAA019022)、广西教育厅项目(201204LX423、2013LX148和KY2015YB280)和中央高校基本科研业务费专项资金(2012017YJSY141)
作者简介:李自尊(1984—),男, 讲师,主要从事微分方程与动力系统与积分不等式的研究,E-mail:zzlqfnu@163.com
更新日期/Last Update: 2018-03-15