×

Bessel’s differential equation and its Hyers-Ulam stability. (English) Zbl 1132.39023

Summary: 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.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Ulam SM: Problems in Modern Mathematics. John Wiley & Sons, New York, NY, USA; 1964:xvii+150. · Zbl 0137.24201
[2] 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 · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222
[3] 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 · Zbl 0398.47040 · doi:10.1090/S0002-9939-1978-0507327-1
[4] Hyers DH, Isac G, Rassias ThM: Stability of Functional Equations in Several Variables. Birkhäuser, Boston, Mass, USA; 1998:vi+313. · Zbl 0907.39025 · doi:10.1007/978-1-4612-1790-9
[5] Hyers DH, Rassias ThM: Approximate homomorphisms.Aequationes Mathematicae 1992,44(2-3):125-153. 10.1007/BF01830975 · Zbl 0806.47056 · doi:10.1007/BF01830975
[6] Jung S-M: Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, Palm Harbor, Fla, USA; 2001:ix+256. · Zbl 0980.39024
[7] Sikorska J: Generalized orthogonal stability of some functional equations.Journal of Inequalities and Applications 2006, 2006: 23 pages. · Zbl 1133.39023 · doi:10.1155/JIA/2006/12404
[8] Liz E, Pituk M: Exponential stability in a scalar functional differential equation.Journal of Inequalities and Applications 2006, 2006: 10 pages. · Zbl 1155.34037 · doi:10.1155/JIA/2006/37195
[9] 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 · Zbl 0918.39009 · doi:10.1155/S102558349800023X
[10] 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 · Zbl 1011.34046 · doi:10.4134/BKMS.2002.39.2.309
[11] Miura T: On the Hyers-Ulam stability of a differentiable map.Scientiae Mathematicae Japonicae 2002,55(1):17-24. · Zbl 1025.47041
[12] 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 · Zbl 1069.34079 · doi:10.4134/JKMS.2004.41.6.995
[13] 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 · Zbl 1039.34054 · doi:10.1002/mana.200310088
[14] 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 · Zbl 1082.39024 · doi:10.1155/JIA.2005.41
[15] 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 · Zbl 1061.34039 · doi:10.1016/j.aml.2003.11.004
[16] 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 · Zbl 1125.34328 · doi:10.1016/j.aml.2005.11.004
[17] 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 · Zbl 1087.34534 · doi:10.1016/j.jmaa.2005.02.025
[18] 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 · Zbl 1106.34032 · doi:10.1016/j.jmaa.2005.07.032
[19] 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 · Zbl 1153.34306
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.