Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 80, pp. 1-11.

Title: Laplace transform and generalized Hyers-Ulam
       stability of linear differential equations

Authors: Qusuay H. Alqifiary (Univ. of Belgrade, Belgrade, Serbia)
         Soon-Mo Jung (Hongik Univ., Sejong, Korea)

Abstract:
 By applying the Laplace transform method, we
 prove that the linear differential equation
 $$
 y^{(n)}(t)+\sum_{k=0}^{n-1}{\alpha_k y^{(k)}(t)}=f(t)
 $$
 has the generalized Hyers-Ulam stability, where $\alpha_k$ is
 a scalar, y and f are n times continuously differentiable
 and of exponential order.

Submitted March 5, 2014. Published March 21, 2014.
Math Subject Classifications: 44A10, 39B82, 34A40, 26D10.
Key Words: Laplace transform method;  differential equations;
           generalized Hyers-Ulam stability.