Electron. J. Diff. Equ., Vol. 2013 (2013), No. 156, pp. 1-8.

Hyers-Ulam stability for Gegenbauer differential equations

Soon-Mo Jung

Abstract:
Using the power series method, we solve the non-homogeneous Gegenbauer differential equation
$$ ( 1 - x^2 )y''(x) + n(n-1)y(x) = \sum_{m=0}^\infty a_m x^m. $$
Also we prove the Hyers-Ulam stability for the Gegenbauer differential equation.

Submitted June 19, 2013. Published July 8, 2013.
Math Subject Classifications: 39B82, 41A30, 34A30, 34A25, 34A05.
Key Words: Gegenbauer differential equation; Hyers-Ulam stability; power series method; second order differential equation.

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Soon-Mo Jung
Mathematics Section, College of Science and Technology
Hongik University, 339-701 Sejong, South Korea
email: smjung@hongik.ac.kr

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