On the stability of linear differential equations of second order

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran

2 Department of Mathematics, Hanyang University, Seoul, 133--791, South Korea

Abstract

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation
$$y''(x)+\alpha y'(x)+\beta y(x)=f(x)$$
in general case, where $y\in C^2[a,b],$  $f\in C[a,b]$ and $-\infty<a<b<+\infty$. The result of this paper improves a result of Li and Shen [\textit{Hyers-Ulam stability of linear differential equations of second order,} Appl. Math. Lett. 23 (2010) 306--309].

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