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 - <p style="text-align: justify;">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.</p>