Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales

Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales

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.

Author Details

Ji Zhang

Zhenxin Liu