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Zbl 1087.34534
Jung, Soon-Mo
Hyers-Ulam stability of linear differential equations of first order. III. (English)
[J] J. Math. Anal. Appl. 311, No. 1, 139-146 (2005). ISSN 0022-247X

Summary: Let $X$ be a complex Banach space and let $I=(a,b)$ be an open interval. In this paper, we prove the generalized Hyers-Ulam stability of the differential equation $ty'(t)+\alpha y(t)+\beta t^rx_0=0$ for the class of continuously differentiable functions $f:I\to X$, where $\alpha, \beta$ and $r$ are complex constants and $x_0$ is an element of $X$. By applying this result, we also prove the Hyers-Ulam stability of the Euler differential equation of second order.

MSC 2000:: *34G10 Linear ODE in abstract spaces

Keywords: Euler differential equation

Cited in: Zbl 1125.34328

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Zentralblatt MATH Berlin [Germany]