Document Type : Research Paper

Authors

• Abbas Najati ¹
• Mohammad Abdollahpour ¹
• Choonkil Park ²

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
$$y^{″}(x)+\alpha y^{\prime }(x)+\beta y(x)=f(x)$$
in general case, where $y\in C^2[a,b],$  $f\in C[a,b]$ and $-\mathrm{\infty }<a<b<+\mathrm{\infty }$. 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].

Keywords

• Hyers-Ulam stability
• linear differential equation of second order