Best constant in Hyers-Ulam stability of first-order homogeneous linear differential equations with a periodic coefficient

被引：31

作者：

Fukutaka, Ryuma ^{[1
]}

Onitsuka, Masakazu ^{[1
]}

机构：

[1] Okayama Univ Sci, Dept Appl Math, Okayama 7000005, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 473卷 / 02期

关键词：

Hyers-Ulam stability; Linear differential equation; Periodic coefficient; Best constant; DYNAMIC EQUATIONS;

D O I：

10.1016/j.jmaa.2019.01.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with Hyers-Ulam stability of the first-order homogeneous linear differential equation x' - a(t)x = 0 on R, where a : R -> R is a continuous periodic function. It is known that if a(t) = 0 then the above equation does not have Hyers-Ulam stability on R. However, sufficient conditions for Hyers-Ulam stability are presented in spite of a(t) has infinitely many zeros and changes sign. Furthermore, the best constant in Hyers-Ulam stability is clarified. To illustrate the obtained results, some examples are included. (C) 2019 The Author(s). Published by Elsevier Inc.

引用

页码：1432 / 1446

页数：15

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