Abstract
In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale {mathbb {T}}={mathbb {R}}) and the case of difference equations (time scale {mathbb {T}}={mathbb {Z}}).
Highlights
The theory of dynamic equations on time scales was introduced by Hilger (1990) in 1988 in order to unify the study of continuous and discrete calculus
In DaCunha (2005), the author studied the stability of the following linear dynamic equation on time scales: x (t) = A(t)x(t), x(t0) = x0, t0 ∈ T
To the best of our knowledge, there are few papers published on the existence and stability of periodic solutions to neutral dynamic equations on time scales
Summary
The theory of dynamic equations on time scales was introduced by Hilger (1990) in 1988 in order to unify the study of continuous and discrete calculus. In DaCunha (2005), the author studied the stability of the following linear dynamic equation on time scales: x (t) = A(t)x(t), x(t0) = x0, t0 ∈ T.
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