HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES

doi:10.1007/s10473-021-0525-2

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1809-1826.doi: 10.1007/s10473-021-0525-2

• 论文 • 上一篇

HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES

Douglas R. ANDERSON¹, Masakazu ONITSUKA²

1. Department of Mathematics, Concordia College, Moorhead, MN 56562 USA;
2. Department of Applied Mathematics, kayama University of Science, Okayama, 700-0005, Japan

收稿日期:2019-05-03 修回日期:2020-10-05 出版日期:2021-10-25 发布日期:2021-10-21
通讯作者: Douglas R. ANDERSON E-mail:andersod@cord.edu
作者简介:Masakazu ONITSUKA,E-mail:onitsuka@xmath.ous.ac.jp
基金资助:
The second author was supported by JSPS KAKENHI Grant Number JP20K03668.

HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES

Douglas R. ANDERSON¹, Masakazu ONITSUKA²

1. Department of Mathematics, Concordia College, Moorhead, MN 56562 USA;
2. Department of Applied Mathematics, kayama University of Science, Okayama, 700-0005, Japan

Received:2019-05-03 Revised:2020-10-05 Online:2021-10-25 Published:2021-10-21
Contact: Douglas R. ANDERSON E-mail:andersod@cord.edu
Supported by:
The second author was supported by JSPS KAKENHI Grant Number JP20K03668.

摘要/Abstract

摘要： We investigate the Hyers-Ulam stability (HUS) of certain second-order linear constant coefficient dynamic equations on time scales, building on recent results for first-order constant coefficient time-scale equations. In particular, for the case where the roots of the characteristic equation are non-zero real numbers that are positively regressive on the time scale, we establish that the best HUS constant in this case is the reciprocal of the absolute product of these two roots. Conditions for instability are also given.

关键词: stability, second order, Hyers-Ulam, time scales

Abstract: We investigate the Hyers-Ulam stability (HUS) of certain second-order linear constant coefficient dynamic equations on time scales, building on recent results for first-order constant coefficient time-scale equations. In particular, for the case where the roots of the characteristic equation are non-zero real numbers that are positively regressive on the time scale, we establish that the best HUS constant in this case is the reciprocal of the absolute product of these two roots. Conditions for instability are also given.

Key words: stability, second order, Hyers-Ulam, time scales

中图分类号:

34N05

Douglas R. ANDERSON, Masakazu ONITSUKA. HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES[J]. 数学物理学报(英文版), 2021, 41(5): 1809-1826.

Douglas R. ANDERSON, Masakazu ONITSUKA. HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES[J]. Acta mathematica scientia,Series B, 2021, 41(5): 1809-1826.

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HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES

HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES

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