含Power的脉冲积分不等式的推广与应用
Generalization and Application of Impulse Integral Inequality with Power
DOI: 10.12677/PM.2017.71002, PDF, HTML, XML, 下载: 1,532  浏览: 2,833  国家自然科学基金支持
作者: 柳长青*, 李自尊：百色学院数学与统计学院，广西 百色
关键词: 脉冲积分不等式；未知函数估计；脉冲微分系统；Impulse Integral Inequalities； Estimation of Unknown Function； Impulsive Differential Systems
摘要: 本文研究了含有幂次的脉冲积分不等式，给出了未知函数的上界估计。利用此结果估计了脉冲微分系统的上界。
Abstract: In this paper, we give the upper bounds estimation of unknown function with power of impulse integral inequality. The result is used to estimate the upper bound of impulsive differential systems.
文章引用：柳长青, 李自尊. 含Power的脉冲积分不等式的推广与应用[J]. 理论数学, 2017, 7(1): 10-15. http://dx.doi.org/10.12677/PM.2017.71002

参考文献

[1] Abdeldaim, A. (2016) Nonlinear Retarded Integral Inequalities of Gronwall-Bellman Type and Applications. Journal of Mathematical Inequalities, 10, 285-299. https://doi.org/10.7153/jmi-10-24
[2] Agarwal, R.P., Deng, S. and Zhang, W. (2005) Generalization of a Retarded Gronwall-Like Inequality and Its Applications. Applied Mathematics and Computation, 165, 599-612. https://doi.org/10.1016/j.amc.2004.04.067
[3] Borysenko, S.D. (1983) About Asymptotical Stability on Linear Approximation of the Systems with Impulse Influence. Ukrainian Mathematical Journal, 35, 144-150.
[4] Borysenko, S.D. (2004) About One Integral Inequality for Piece-Wise Continuous Functions. Proceedings of X International Kravchuk Conference, Kyiv, 323.
[5] Borysenko, S.D., Ciarletta, M. and Iovane, G. (2005) Integro-Sum Inequalities and Motion Stability of Systems with Impulse Perturbations. Nonlinear Analysis, 62, 417-428. https://doi.org/10.1016/j.na.2005.03.032
[6] Gllo, A. and Piccirilo, A.M. (2007) About New Analogies of Gronwall-Bellman-Bihari Type Inequalities for Discontinuous Functions and Estimated Solutions for Impulsive Differential Systems. Nonlinear Analysis, 67, 1550-1559. https://doi.org/10.1016/j.na.2006.07.038
[7] Gllo, A. and Piccirilo, A.M. (2009) About Some New Generalizations of Bell-man-Bihari Results for Integro-Func- tional Inequalities with Discontinuous Functions and Applications. Nonlinear Analysis, 71, e2276-e2287. https://doi.org/10.1016/j.na.2009.05.019
[8] Iovane, G. (2007) Some New Integral Inequalities of Bellman-Bihari Type with Delay for Discontinuous Functions. Nonlinear Analysis, 66, 498-508. https://doi.org/10.1016/j.na.2005.11.043
[9] 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.
[10] 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): 4-8.
[11] 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): 161-166.
[12] Mi, Y.Z., Deng, S.F. and Li, X.P. (2013) Nonlinear Integral Inequalities with Delay for Discontinuous Functions and Their Applications. Journal of Inequalities and Applications, 2013, 11 p.
[13] 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.
[14] Wang, W.S. (2007) A Generalized Retarded Gronwall-Like Inequality in Two Variables and Applications to BVP. Applied Mathematics and Computation, 191, 144-154. https://doi.org/10.1016/j.amc.2007.02.099
[15] Wang, W.S. and Li, Z.Z. (2011) A New Class of Impulsive Integral Inequalities and Its Application. 2011 International Conference on Multimedia Technology (ICMT 2011), 3, 1897-1899. https://doi.org/10.1109/ICMT.2011.6002439
[16] 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.
[17] Zheng, Z.W., Gao, X. and Shao, J. (2016) Some New Generalized Retarded Inequalities for Discontinuous Functions and Their Applications. Journal of Inequalities and Applications, 2016, 14 p.

为你推荐