Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales
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@Article{CMR-27-24,
author = {Zhang , Ji and Liu , Zhenxin},
title = {Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {27},
number = {1},
pages = {24--36},
abstract = {
In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation $x^∆ = A(t)x$ on time scales. Moreover, for the nonlinear perturbed equation $x^∆ = A(t)x + f(t, x)$ we give the instability of the zero solution when $f$ is sufficiently small.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19110.html} }
TY - JOUR
T1 - Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales
AU - Zhang , Ji
AU - Liu , Zhenxin
JO - Communications in Mathematical Research
VL - 1
SP - 24
EP - 36
PY - 2021
DA - 2021/05
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19110.html
KW - quadratic Lyapunov function, exponential dichotomy, time scale, instability.
AB -
In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation $x^∆ = A(t)x$ on time scales. Moreover, for the nonlinear perturbed equation $x^∆ = A(t)x + f(t, x)$ we give the instability of the zero solution when $f$ is sufficiently small.
Ji Zhang & Zhenxin Liu. (2021). Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales.
Communications in Mathematical Research . 27 (1).
24-36.
doi:
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