On the Exponential Stability of the Implicit Differential Systems in Hilbert Spaces

被引：0
|
作者：
Beghersa, Nor El-Houda [1 ]
Benabdallah, Mehdi [1 ]
Hariri, Mohamed [2 ]
机构：
[1] Univ Sci & Technol Oran Mohamed Boudiaf USTO MB, Fac Math & Comp Sci, Dept Math, BP 1505 El-MNOUAR, Bir El Djir 31000, Oran, Algeria
[2] Ain Temouchent Univ, Dept Math, Mohamed Hariri, Ain Temouchent 46000, Algeria
来源：
INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS | 2023年 / 21卷
关键词：
spectral theory; operator pencil; stability; implicit system;
D O I：
10.28924/2291-8639-21-2023-54
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The aim of this research is to study the exponential stability of the stationary implicit system: Ax'(t) + Bx(t) = 0, where A and B are bounded operators in Hilbert spaces. The achieved results are the generalization of Liapounov Theorem for the spectrum of the operator pencil ?A + B. We also establish the exponential stability conditions for the corresponding perturbed and quasi-linear implicit systems.
引用
收藏
页数：9
相关论文
共 50 条
  • [31] Implicit Regularization of Accelerated Methods in Hilbert Spaces
    Pagliana, Nicolo
    Rosasco, Lorenzo
    ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 32 (NIPS 2019), 2019, 32
  • [32] Lyapunov theorems for exponential dichotomies in Hilbert spaces
    Dragicevic, Davor
    Preda, Ciprian
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2016, 27 (04)
  • [33] Exponential Stability of Impulsive Stochastic Delay Differential Systems
    Wu, Xiaotai
    Yan, Litan
    Zhang, Wenbing
    Chen, Liang
    DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2012, 2012
  • [34] ON THE Ψ-EXPONENTIAL ASYMPTOTIC STABILITY OF NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS
    Diamandescu, Aurel
    ANALELE STIINTIFICE ALE UNIVERSITATII AL I CUZA DIN IASI-SERIE NOUA-MATEMATICA, 2012, 58 (02): : 279 - 292
  • [35] UNIFORM EXPONENTIAL STABILITY OF IMPULSIVE DELAY DIFFERENTIAL SYSTEMS
    Gupta, Bhanu
    Srivastava, Sanjay K.
    Mahajan, Aakanksha
    ADVANCES IN DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES, 2009, 4 (01): : 29 - 39
  • [36] Exponential Stability of Impulsive Stochastic Functional Differential Systems
    Wu, Zheng
    Huang, Hao
    Wang, Lianglong
    ABSTRACT AND APPLIED ANALYSIS, 2012,
  • [37] Exponential Stability of Impulsive Differential Systems with Variable Delays
    Wang, Huamin
    Duan, Shukai
    Huang, Tingwen
    Wang, Lidan
    PROCEEDINGS OF THE 2016 12TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION (WCICA), 2016, : 1675 - 1680
  • [38] ON STABILITY OF BASES IN HILBERT SPACES
    Larionov, E. A.
    EURASIAN MATHEMATICAL JOURNAL, 2020, 11 (02): : 65 - 71
  • [39] ON STABILITY AND BOUNDEDNESS OF DIFFERENTIAL SYSTEMS IN BANACH SPACES
    TSOKOS, CP
    RAO, MRM
    PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1969, 65 : 507 - &
  • [40] EXPONENTIAL STABILITY OF LINEAR AND ALMOST PERIODIC SYSTEMS ON BANACH SPACES
    Buse, Constantin
    Lupulescu, Vasile
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2003,
12345