具有初边值条件的集值脉冲微分方程的平均法

具有初边值条件的集值脉冲微分方程的平均法

The Averaging Method of Set Impulsive Differential Equations with Initial and Boundary Value Conditions

摘要/Abstract

参考文献 28

Metrics

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1504-1515.

王培光*(),杨凯愉()

^{河北大学数学与信息科学学院河北保定 071002}

收稿日期:2020-04-24 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 王培光 E-mail:pgwang@hbu.edu.cn;15932002803@163.com
作者简介:杨凯愉, E-mail: 15932002803@163.com
基金资助:
国家自然科学基金(11771115);国家自然科学基金(12171135)

Peiguang Wang*(),Kaiyu Yang()

^{College of Mathematics and Information Science, Hebei University, Hebei Baoding 071002}

Received:2020-04-24 Online:2021-10-26 Published:2021-10-08
Contact: Peiguang Wang E-mail:pgwang@hbu.edu.cn;15932002803@163.com
Supported by:
the NSFC(11771115);the NSFC(12171135)

摘要：

该文应用全局平均法和局部加法平均法，研究了欧氏空间 $\mathbb{R}^{n}$ 中具有初值和多点边值问题的集值脉冲微分方程，证明了两类问题的原方程与平均方程之间解的近似关系.

关键词: 集值微分方程, 多点边值, 脉冲, 平均法

Abstract:

This paper uses the scheme of full, and partially additive averaging method to study the set impulsive differential equations with the initial and multipoint boundary value problems in Euclidean space $\mathbb{R}^{n}$ , and proves the approximate relationship of the solutions between the original equations and the average equations.

Key words: Set differential equations, Multipoint boundary value, Impulse, Averaging method

中图分类号:

O175.12

王培光,杨凯愉. 具有初边值条件的集值脉冲微分方程的平均法[J]. 数学物理学报, 2021, 41(5): 1504-1515.

Peiguang Wang,Kaiyu Yang. The Averaging Method of Set Impulsive Differential Equations with Initial and Boundary Value Conditions[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1504-1515.

1	Bainov D , Domshlak Y , Milusheva S . Partial averaging for impulsive differential equations with supremum. Georgian Mathematical Journal, 1996, 3 (1): 11- 26 doi: 10.1515/GMJ.1996.11
2	Bainov D , Milusheva S . Application of the averaging method for functional-differential equations with impulses. J Math Anal Appl, 1983, 95, 85- 105 doi: 10.1016/0022-247X(83)90137-3
3	Bainov D , Simeonov P . Impulsive Differential Equations. Singapore: World Scientific, 1995
4	Bainov D , Simeonov P . Systems with Impulsive Effect: Stability, Theory and Applications. New York: Halsted Press, 1998
5	Benchohra M , Boucherif A . An existence result for first order initial value problems for impulsive differential inclusions in Banach spaces. Archivum Mathematicum (Brno), 2000, 36, 159- 169
6	Devi J V . Basic results in impulsive set differential equations. Nonlinear Studies, 2003, 10 (3): 259- 271
7	Devi J V , Vatsala A S . A study of set differential equations with delay. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 2004, 11, 287- 300
8	Federson M , Mesquita J G . Non-periodic averaging principles for measure functional differential equations and functional dynamic equations on time scales involving impulses. J Differential Equations, 2013, 255, 3098- 3126 doi: 10.1016/j.jde.2013.07.026
9	Kitanov N . Method of averaging for optimal control problems with impulsive effects. Inter J Pure Appl Math, 2011, 72 (4): 573- 589
10	Klymchuk S , Plotnikov A , Skripnik N . Overview of V.A. Plotnikov's research on averaging of differential inclusions. Physica D, 2012, 241 (22): 1932- 1947 doi: 10.1016/j.physd.2011.05.004
11	刘健, 张志信, 蒋威. 分数阶非线性时滞脉冲微分系统的全局Mittag-Leffler稳定性. 数学物理学报, 2020, 40A (4): 1053- 1060 doi: 10.3969/j.issn.1003-3998.2020.04.020
	Liu J , Zhang Z X , Jiang W . Global mittag-leffler stability of fractional order nonlinear impulsive differential systems with time delay. Acta Math Sci, 2020, 40A (4): 1053- 1063 doi: 10.3969/j.issn.1003-3998.2020.04.020
12	Lakshmikantham V , Bainov D , Simeonov P . Theory of Impulsive Differential Equations. Singapore: World Scientific, 1989
13	Lakshmikantham V , Bhaskar T G , Devi J V . Theory of Set Differential Equations in Metric Spaces. Cambridge: Cambridge Scientific Publisher, 2005
14	罗艳, 谢文哲. 上下解反向的脉冲微分包含解的存在性. 数学物理学报, 2019, 39A (5): 1055- 1063 doi: 10.3969/j.issn.1003-3998.2019.05.008
	Luo Y , Xie W Z . Existence of solution for impulsive differential inclusions with upper and lower solutions in the reverse order. Acta Math Sci, 2019, 39A (5): 1055- 1063 doi: 10.3969/j.issn.1003-3998.2019.05.008
15	Mil'man V D , Myshkis A D . On the stability of motion in the presence of impulses. Siberian Math J, 1960, 1, 233- 237
16	Plotnikova N . Averaging of impulsive differential inclusions. Mat Stud, 2005, 23 (1): 52- 56
17	Plotnikov V A , Ivanov R P , Kitanov N M . Method of averaging for impulsive differential inclusions. Pliska Stud Math Bulg, 1998, 12, 191- 200
18	Plotnikov V A , Komleva T . Averaging of set integro-differential equations. Applied Mathematics, 2011, 1 (2): 99- 105
19	Plotnikov V A , Plotnikova L I . Averaging of differential inclusions with many-valued pulses. Ukrainian Mathematical Journal, 1995, 47 (11): 1741- 1749 doi: 10.1007/BF01057922
20	Perestyuk N A , Plotnikov V A , Samoilenko A M , Skripnik N V . Differential Equations with Impulse Effects: Multivalued Right-Hand Sides with Discontinuities. Berlin: De Gruyter, 2011
21	Plotnikov V A , Rashkov P I . Averaging in differential equations with Hukuhara derivative and delay. Functional Differential Equations, 2001, 3 (4): 371- 381
22	Perestyuk N A , Skripnik N V . Averaging of set-valued impulsive systems. Ukrainian Mathematical Journal, 2013, 65 (1): 140- 157 doi: 10.1007/s11253-013-0770-1
23	Samoilenko A M , Perestyuk N A . Impulsive Differential Equations. Singapore: World Scientific, 1995
24	Skripnik N V . Averaging of impulsive differential inclusions with Hukuhara derivative. Nonlinear Oscil, 2007, 10 (3): 422- 438 doi: 10.1007/s11072-007-0033-x
25	Skrypnyk N V . On the averaging method for differential equations with Hukuhara's derivative. Visn Cherniv Nats Univ, 2008, 374, 109- 115
26	Skripnik N V . The full averaging of fuzzy impulsive differential inclusions. Surv Math Appl, 2010, 5, 247- 263
27	Skripnik N V . The partial averaging of fuzzy impulsive differential inclusions. Different Integr Equat, 2011, 24 (7/8): 743- 758
28	Skripnik N V . Averaging of impulsive differential inclusions with fuzzy right-hand side when the average is absent. Asian-European Journal of Mathematics, 2015, 8 (4): 1550086 doi: 10.1142/S1793557115500862

Just accepted

Online first

Just accepted

Online first

Viewed

Full text

From	Others	local

Times	1	94
Rate	1%	99%

Abstract

Just accepted	Online first	Issue

0	0	96

From	Others	local

Times	92	4
Rate	96%	4%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

[1]	杨静,柯昌成,魏周超. 一类连续和不连续分段线性系统的周期解研究[J]. 数学物理学报, 2021, 41(4): 1053-1065.
[2]	蒋婷婷,杜增吉. 带有脉冲和Holling-IV型功能反应函数的中立型捕食-食饵模型的周期解[J]. 数学物理学报, 2021, 41(1): 178-193.
[3]	闫朝琳,高建芳. 混合型脉冲微分方程的数值振动性分析[J]. 数学物理学报, 2020, 40(4): 993-1006.
[4]	刘健,张志信,蒋威. 分数阶非线性时滞脉冲微分系统的全局Mittag-Leffler稳定性[J]. 数学物理学报, 2020, 40(4): 1053-1060.
[5]	姚旺进. 基于变分方法的脉冲微分方程耦合系统解的存在性和多重性[J]. 数学物理学报, 2020, 40(3): 705-716.
[6]	罗李平,罗振国,曾云辉. 一类非线性脉冲中立抛物型分布参数系统的振动条件[J]. 数学物理学报, 2020, 40(3): 784-795.
[7]	刘玉记. 含三个Riemann-Liouville分数阶导数的脉冲Langevin型方程的边值问题的可解性[J]. 数学物理学报, 2020, 40(1): 103-131.
[8]	朱昆,沈建和. 一类广义Gierer-Meinhardt方程多脉冲同宿解的再研究[J]. 数学物理学报, 2019, 39(6): 1365-1375.
[9]	罗艳,谢文哲. 上下解反向的脉冲微分包含解的存在性[J]. 数学物理学报, 2019, 39(5): 1055-1063.
[10]	付盈洁,蓝桂杰,张树文,魏春金. 污染环境下具有脉冲输入的随机捕食-食饵模型的动力学研究[J]. 数学物理学报, 2019, 39(3): 674-688.
[11]	陈苗苗,裴永珍,梁西银,吕云飞. 害虫治理SI模型的最优脉冲控制策略[J]. 数学物理学报, 2019, 39(3): 689-704.
[12]	朱波,刘立山. 带瞬时脉冲的分数阶非自制发展方程解的存在唯一性[J]. 数学物理学报, 2019, 39(1): 105-113.
[13]	王惠文, 曾红娟, 李芳. 多基点分数阶微分方程脉冲边值问题解的存在性[J]. 数学物理学报, 2018, 38(4): 697-715.
[14]	廖暑芃, 沈建和. 一类带有慢变参数的sine-Gordon方程的单脉冲异宿轨道[J]. 数学物理学报, 2018, 38(4): 810-822.
[15]	罗李平, 罗振国, 邓义华. 脉冲扰动对非线性时滞双曲型分布参数系统振动的影响[J]. 数学物理学报, 2018, 38(2): 313-321.