Laplace transform and Hyers-Ulam stability of linear differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Rezaei, Hamid¹  Jung, Soon-Mo²  Rassias, Themistocles M.³ 

[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

关键词: Laplace transform;    Laplace transform method;    Differential equation;    Hyers-Ulam stability;    Approximation;   

DOI  :  10.1016/j.jmaa.2013.02.034

来源: Elsevier

【 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.

【 授权许可】

Free