@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} }