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Volume 27, Issue 1
Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales

Ji Zhang & Zhenxin Liu

Commun. Math. Res., 27 (2011), pp. 24-36.

Published online: 2021-05

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  • 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.

  • Keywords

quadratic Lyapunov function, exponential dichotomy, time scale, instability.

  • AMS Subject Headings

34N05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-24, author = {Ji and Zhang and and 18342 and and Ji Zhang and Zhenxin and Liu and and 18343 and and Zhenxin Liu}, 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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