Please wait a minute...
浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (2): 181-183    DOI: 10.3785/j.issn.1008-9497.2016.02.010
数学与计算机科学     
巴拿赫空间上斜演化半流的非一致指数不稳定性的存在条件
岳田1, 宋晓秋2
1. 湖北汽车工业学院理学院, 湖北十堰 442002;
2. 中国矿业大学理学院, 江苏徐州 221116
Criteria for the existence of nonuniform exponential instability of skew-evolution semiflows in Banach spaces
YUE Tian1, SONG Xiaoqiu2
1. School of Science, Hubei University of Automotive Technology, Shiyan 442002, Hubei Province, China;
2. College of Science, China University of Mining and Technology, Xuzhou 221116, Jiangsu Province, China
 全文: PDF(1085 KB)  
摘要： 基于一致指数不稳定的定义,引入了Banach空间中斜演化半流非一致指数不稳定的概念,并用实例阐释了二者的关系.借助于指数稳定性的研究方法,讨论了斜演化半流非一致指数不稳定的特征,建立了其非一致指数不稳定的2个充要条件.所得结论推广了指数稳定性及一致指数不稳定性中的一些已有结果.
关键词： 斜演化半流;  非一致指数不稳定性;  巴拿赫空间;  指数衰退    
Abstract: Based on the definition of uniform exponential instability, a skew-evolution semiflow with nonuniform exponential instability is presented in Banach spaces. An illustrating example is used to clarify the relationship between the two concepts. Exponential stability technique is applied to study the features of nonuniform exponential instability of skew-evolution semilflows. Two necessary and sufficient conditions concerning the nonuniform exponential instability of skew-evolution semiflows are given. The obtained conclusions are generalizations of the well-known results about the exponential stability and uniform exponential instability.
Key words: skew-evolution semiflow    nonuniform exponential instability    Banach space    exponential decay
收稿日期: 2015-08-06 出版日期: 2016-03-12
CLC:  O175.13  
基金资助: 湖北省自然科学基金资助项目(2014CFB629);湖北汽车工业学院校预研基金项目(2014CFB629).
作者简介: 岳田(1988-),ORCID:http://orcid.org/0000-0002-3371-5673,男,助教,硕士,主要从事微分系统的渐近行为研究,E-mail:ytcumt@163.com.
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章　　
岳田
宋晓秋

引用本文:

岳田, 宋晓秋. 巴拿赫空间上斜演化半流的非一致指数不稳定性的存在条件[J]. 浙江大学学报（理学版）, 2016, 43(2): 181-183.

YUE Tian, SONG Xiaoqiu. Criteria for the existence of nonuniform exponential instability of skew-evolution semiflows in Banach spaces. Journal of ZheJIang University(Science Edition), 2016, 43(2): 181-183.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.02.010    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I2/181

[1] MEGAN M, STOICA C. Exponential instability of skew-evolution semiflows in Banach spaces[J]. Stud Univ Babes-Bolyai Math,2008,53(1):17-24.
[2] STOICA C, MEGAN M. On uniform exponential stability for skew-evolution semiflows on Banach spaces[J]. Nolinear Analysis,2010,72(3/4):1305-1313.
[3] HAI P H. Continuous and discrete characterizations for the uniform exponential stability of linear skew-evolution semiflows[J]. Nolinear Anal,2010,72(12):4390-4396.
[4] HAI P H. Discrete and continuous versions of Barbashin-type theorems of linear skew-evolution semiflows[J]. Appl Anal,2011,90(12):1897-1907.
[5] STOICA C, MEGAN M. On nonuniform exponential stability for skew-evolution semiflows in Banach spaces[J]. Carpathian J Math,2013,29(2):259-266.
[6] STOICA C, BORLEA D. Exponential stability versus polynomial stability for skew-evolution semiflows in infinite dimensional spaces[J]. Theory Appl Math Comput Sci,2014,4(2):221-229.
[7] DATKO R. Uniform asymptotic stability of evolutionary processes in Banach spaces[J]. SIAM J Math Anal,1972,3(3):428-445.
[8] YUE T, SONG X Q, LI D Q. On weak exponential expansiveness of skew-evolution semiflows in Banach spaces[J]. J Inequal Appl,2014(1):1-11.
[9] YUE T, LEI G L, SONG X Q. Some characterizations for the uniform exponential expansiveness of linear skew-evolution semiflows[J]. Advances in Mathematics (China),2015,45,doi:10.11845/sxjz.2014173b.
[1] 岳田, 宋晓秋. 线性斜积半流的一致指数稳定性的若干刻画[J]. 浙江大学学报（理学版）, 2018, 45(5): 545-548.