Laplace transform and Hyers-Ulam stability of linear differential equations

被引：93
|
作者：
Rezaei, Hamid [1 ]
Jung, Soon-Mo [2 ]
Rassias, Themistocles M. [3 ]
机构：
[1] Univ Yasuj, Dept Math, Coll Sci, Yasuj 7591474831, Iran
[2] Hongik Univ, Math Sect, Coll Sci & Technol, Sejong 339701, South Korea
[3] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 403卷 / 01期
关键词：
Laplace transform; Laplace transform method; Differential equation; Hyers-Ulam stability; Approximation; CONSTANT-COEFFICIENTS; 1ST-ORDER; OPERATORS;
D O I：
10.1016/j.jmaa.2013.02.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove the Hyers-Ulam stability of a linear differential equation of the nth order. More precisely, applying the Laplace transform method, we prove that the differential equation y((n)) (t) + Sigma(n-1)(k=0) alpha(k)y((k)) (t) = f(t) has Hyers-Ulam stability, where alpha(k) is a scalar, y and f are n times continuously differentiable and of exponential order, respectively. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：244 / 251
页数：8
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