Abstract
In this paper, for affine periodic systems on time scales, we establish LaSalle stationary oscillation theorem to obtain the existence and asymptotic stability of affine periodic solutions on time scales. As applications, we present the existence and asymptotic stability of affine periodic solutions on time scales via Lyapunov’s method.
Highlights
1 Introduction and statement of the main result The research of periodic phenomena has a long history that started with Kepler and Newton when they studied orbits of planets in the solar system
In 1892, Lyapunov introduced the concept of stability of a dynamic system and created Lyapunov’s second method in the study of stability
The main goal of this paper is to discuss the existence of affine periodic solutions and asymptotic stability of affine periodic systems on time scales by LaSalle-type stationary oscillation principle
Summary
1 Introduction and statement of the main result The research of periodic phenomena has a long history that started with Kepler and Newton when they studied orbits of planets in the solar system. The existence of solutions of dynamic equations on time scales has been extensively investigated, especially concerning periodicity. The main goal of this paper is to discuss the existence of affine periodic solutions and asymptotic stability of affine periodic systems on time scales by LaSalle-type stationary oscillation principle. Where f : T × Rn → Rn is an rd-continuous function, T is a T -periodic time scale.
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