基于指数型二分性的二阶线性微分方程解的渐近性质研究  

On the Asymptotic Behavior of Solutions for the Second Order LinearDifferential Equations Via Exponential Dichotomy

作　　者：郑航 夏永辉 ZHENG Hang;XIA Yong-hui(Department of Mathematics and Computer, Wuyi University, Wuyishan Fujian 354300, China;Department of Mathematics, Zhejiang Normal University, Jinhua Zhejiang 321004, China)

机构地区：[1]武夷学院数学与计算机学院,福建武夷山354300 [2]浙江师范大学数学与计算机科学学院,浙江金华321004

出　　处：《大学数学》2020年第5期93-100,共8页College Mathematics

基　　金：福建省教育厅中青年教师教育科研项目(JT180558)。

摘　　要：不同于文[1]的证明方法,利用指数型二分性理论研究常微分方程中一类二阶常系数线性微分方程解的渐近性质,获得该微分方程存在有界解的充分条件,且证有界解唯一.又进一步探讨了特征根具有正实部的情况,并将正向有界推广到任意区间有界.Different from the method in[1],this paper studies the behavior of solutions for a class of second-order linear differential equations with constant coefficients in ordinary differential equations via exponential dichotomy.A sufficient condition for the existence of unique bounded solution of the second order differential equation is obtained.And we prove that the bounded solution is unique.We further discuss the case when the real part of the eigenvalues are positive.Moreover,we extend the bounded solution to the whole axis.

关 键 词：指数型二分性 有界解 微分方程 

分 类 号：O172.1[理学—数学]