Abstract
Abstract In this paper, by using a fixed point theorem and the theory of calculus on time scales, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of Hamiltonian systems on time scales. We also present numerical examples to show the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even if the time scale T = R or ℤ.
Highlights
Hamiltonian system, which was introduced by the Irish mathematician SWR Hamilton, is widely used in mathematical sciences, life sciences and so on
Most existing results on the study of Hamiltonian systems are for continuous systems
There have been some results devoted to Hamiltonian systems on time scales [, – ]
Summary
Hamiltonian system, which was introduced by the Irish mathematician SWR Hamilton, is widely used in mathematical sciences, life sciences and so on. Most existing results on the study of Hamiltonian systems are for continuous systems. It is meaningful to study dynamical systems on time scales (see [ – ] and references cited therein), which helps avoid proving results twice, once for differential equations and once for difference equations.
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