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Hyers-Ulam stability of linear differential equations of first order, III
- Authors
- Jung, SM
- Issue Date
- Nov-2005
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Hyers-Ulam stability; linear differential equation; Euler equation
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.311, no.1, pp.139 - 146
- Journal Title
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Volume
- 311
- Number
- 1
- Start Page
- 139
- End Page
- 146
- ISSN
- 0022-247X
- Abstract
- Let X be a complex Banach space and let I = (a, b) be an open interval. In this paper, we will prove the generalized Hyers-Ulam stability of the differential equation ty'(t) +alpha y(t) + beta t(r)x(0) = 0 for the class of continuously differentiable functions f : I -> 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. (c) 2005 Elsevier Inc. All rights reserved.
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