- Research Article
- Open access
- Published:
Bessel's Differential Equation and Its Hyers-Ulam Stability
Journal of Inequalities and Applications volume 2007, Article number: 021640 (2007)
Abstract
We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation.
References
Ulam SM: Problems in Modern Mathematics. John Wiley & Sons, New York, NY, USA; 1964:xvii+150.
Hyers DH: On the stability of the linear functional equation. Proceedings of the National Academy of Sciences of the United States of America 1941, 27: 222–224. 10.1073/pnas.27.4.222
Rassias ThM: On the stability of the linear mapping in Banach spaces. Proceedings of the American Mathematical Society 1978,72(2):297–300. 10.1090/S0002-9939-1978-0507327-1
Hyers DH, Isac G, Rassias ThM: Stability of Functional Equations in Several Variables. Birkhäuser, Boston, Mass, USA; 1998:vi+313.
Hyers DH, Rassias ThM: Approximate homomorphisms. Aequationes Mathematicae 1992,44(2–3):125–153. 10.1007/BF01830975
Jung S-M: Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, Palm Harbor, Fla, USA; 2001:ix+256.
Sikorska J: Generalized orthogonal stability of some functional equations. Journal of Inequalities and Applications 2006, 2006: 23 pages.
Liz E, Pituk M: Exponential stability in a scalar functional differential equation. Journal of Inequalities and Applications 2006, 2006: 10 pages.
Alsina C, Ger R: On some inequalities and stability results related to the exponential function. Journal of Inequalities and Applications 1998,2(4):373–380. 10.1155/S102558349800023X
Takahasi S-E, Miura T, Miyajima S: On the Hyers-Ulam stability of the Banach space-valued differential equation. Bulletin of the Korean Mathematical Society 2002,39(2):309–315. 10.4134/BKMS.2002.39.2.309
Miura T: On the Hyers-Ulam stability of a differentiable map. Scientiae Mathematicae Japonicae 2002,55(1):17–24.
Miura T, Jung S-M, Takahasi S-E: Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations. Journal of the Korean Mathematical Society 2004,41(6):995–1005. 10.4134/JKMS.2004.41.6.995
Miura T, Miyajima S, Takahasi S-E: Hyers-Ulam stability of linear differential operator with constant coefficients. Mathematische Nachrichten 2003,258(1):90–96. 10.1002/mana.200310088
Jung S-M: Hyers-Ulam stability of Butler-Rassias functional equation. Journal of Inequalities and Applications 2005,2005(1):41–47. 10.1155/JIA.2005.41
Jung S-M: Hyers-Ulam stability of linear differential equations of first order. Applied Mathematics Letters 2004,17(10):1135–1140. 10.1016/j.aml.2003.11.004
Jung S-M: Hyers-Ulam stability of linear differential equations of first order, II. Applied Mathematics Letters 2006,19(9):854–858. 10.1016/j.aml.2005.11.004
Jung S-M: Hyers-Ulam stability of linear differential equations of first order, III. Journal of Mathematical Analysis and Applications 2005,311(1):139–146. 10.1016/j.jmaa.2005.02.025
Jung S-M: Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients. Journal of Mathematical Analysis and Applications 2006,320(2):549–561. 10.1016/j.jmaa.2005.07.032
Jung S-M: Legendre's differential equation and its Hyers-Ulam stability. to appear in Abstract and Applied Analysis to appear in Abstract and Applied Analysis
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Kim, B., Jung, SM. Bessel's Differential Equation and Its Hyers-Ulam Stability. J Inequal Appl 2007, 021640 (2007). https://doi.org/10.1155/2007/21640
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2007/21640