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

页码：244 / 251

页数：8

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