Existence and uniqueness of almost periodic solutions for a class of nonlinear Duffing system with time-varying delays

Yanli Xu

doi:10.14232/ejqtde.2012.1.80

Abstract

Existence and uniqueness of almost periodic solutions for a class of nonlinear Duffing system with time-varying delays

Highlights

In recent years, the dynamic behaviors of nonlinear Duffing equations have been widely investigated in [1,2,3,4] due to the application in many fields such as physics, mechanics, engineering, other scientific fields
Some results on existence of the almost periodic solutions were obtained in the literature
By Lemma 1.2, we obtain that the system (2.2) has exactly one almost periodic solution:

Summary

Introduction

The dynamic behaviors of nonlinear Duffing equations have been widely investigated in [1,2,3,4] due to the application in many fields such as physics, mechanics, engineering, other scientific fields In such applications, it is important to know the existence of the almost periodic solutions for nonlinear Duffing equations. Is said to admit an exponential dichotomy on R if there exist positive constants k, α, projection P and the fundamental solution matrix X(t) of (1.8) satisfying. [10,11] Let Q(t) = (qij) be an n × n almost periodic matrix defined on R and let there exist a positive constant ν such that n. Lemma 1.2. [10,11] If the linear system (1.8) admits an exponential dichotomy, the almost periodic system dz(t) dt

Existence and uniqueness of almost periodic solutions

An example