Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales (Communications in Mathematical Research, 2021)
In this paper, we study the relationship between exponential dichotomyand 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 theinstability of the zero solution when $f$ is sufficiently small.