Year: 2011
Author: Ji Zhang, Zhenxin Liu
Communications in Mathematical Research , Vol. 27 (2011), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-CMR-19110
Communications in Mathematical Research , Vol. 27 (2011), Iss. 1 : pp. 24–36
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: quadratic Lyapunov function exponential dichotomy time scale instability.