Electron. J. Diff. Equ., Vol. 2014 (2014), No. 80, pp. 1-11.

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

Qusuay H. Alqifiary, Soon-Mo Jung

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.

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Qusuay H. Alqifiary
Department of Mathematics, University of Belgrade, Belgrade, Serbia.
University of Al-Qadisiyah, Al-Diwaniya, Iraq
email: qhaq2010@gmail.com
Soon-Mo Jung
Mathematics Section
College of Science and Technology
Hongik University, 339--701 Sejong, Korea
email: smjung@hongik.ac.kr

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