Invariance of Hyers-Ulam stability of linear differential equations and its applications

We prove that the generalized Hyers-Ulam stability of linear differential equations of n th order (defined on I ) is invariant under any monotone one-to-one correspondence τ : I → J which is n times continuously differentiable. Moreover, using this result, we investigate the generalized Hyers-Ulam s...

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Bibliographic Details
Published in:Advances in difference equations 2015-09, Vol.2015 (1), p.1-14, Article 277
Main Authors: Choi, Ginkyu, Jung, Soon-Mo
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Difference equations
Differential equations
Functional Analysis
Invariance
Invariants
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Stability
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Summary:We prove that the generalized Hyers-Ulam stability of linear differential equations of n th order (defined on I ) is invariant under any monotone one-to-one correspondence τ : I → J which is n times continuously differentiable. Moreover, using this result, we investigate the generalized Hyers-Ulam stability of the linear differential equation of second order and the Cauchy-Euler equation.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-015-0617-1