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Year 2018, Volume: 2 Issue: 2, 106 - 112, 30.06.2018
https://doi.org/10.31197/atnaa.402721

Abstract

References

  • [1] G.L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Mathematicae,50(1995), 143-190.[2] D.H. Hyers, G. Isac, Th.M. Rassias, Stability of Functional Equations in Several Variables,Birkhäuser, Boston, 1998.[3] S.M. Jung, H. Şevli, Power series method and approximate linear differential equations of secondorder, Adv. Difference Equ., (2013), 1-9.[4] B. Kim, S.M. Jung, Bessel’s differential equation and its Hyers-Ulam stability, J. Ineq. Appl.,(2007), 8 pages.[5] T. Miura, S. Miyajima, S. E. Takahasi, A characterization of Hyers-Ulam stability of first orderlinear differential operators, J. Math. Anal. Appl., 286(2003), 136-146.[6] M. Obłoza, Hyers-Ulam stability of the linear differential equation, Rocznik Nauk.-Dydakt.Prace Mat., 13(1993), 259-270.[7] M. Obłoza, Connections between Hyers and Lyapunov stability of the ordinary differential equations,Rocznik Nauk.-Dydakt. Prace Mat., 14(1997), 141-146.[8] D. Popa, I. Raşa, On the Hyers-Ulam stability of the linear differential equation, J. Math. Anal.Appl., 381(2011), 530-537.[9] D. Popa, I. Raşa, Hyers-Ulam stability of the linear differential operator with nonconstantcoefficients, Appl. Math. Comput., 219(2012), 1562-1568.[10] D. Popa, G. Pugna, I. Raşa, Bounds of solutions of some differential equations and Ulamstability, submitted.[11] I. Raşa, Entropies and Heun functions associated with positive linear operators, Appl. Math.Comput., 268 (2015), 422-431.[12] S.M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1960.

On Ulam stability of the second order linear differential equation

Year 2018, Volume: 2 Issue: 2, 106 - 112, 30.06.2018
https://doi.org/10.31197/atnaa.402721

Abstract

We obtain a result on Ulam stability for a linear differential equation
in Banach spaces. As application we give a result on the stability of Heun’s
differential equation.

References

  • [1] G.L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Mathematicae,50(1995), 143-190.[2] D.H. Hyers, G. Isac, Th.M. Rassias, Stability of Functional Equations in Several Variables,Birkhäuser, Boston, 1998.[3] S.M. Jung, H. Şevli, Power series method and approximate linear differential equations of secondorder, Adv. Difference Equ., (2013), 1-9.[4] B. Kim, S.M. Jung, Bessel’s differential equation and its Hyers-Ulam stability, J. Ineq. Appl.,(2007), 8 pages.[5] T. Miura, S. Miyajima, S. E. Takahasi, A characterization of Hyers-Ulam stability of first orderlinear differential operators, J. Math. Anal. Appl., 286(2003), 136-146.[6] M. Obłoza, Hyers-Ulam stability of the linear differential equation, Rocznik Nauk.-Dydakt.Prace Mat., 13(1993), 259-270.[7] M. Obłoza, Connections between Hyers and Lyapunov stability of the ordinary differential equations,Rocznik Nauk.-Dydakt. Prace Mat., 14(1997), 141-146.[8] D. Popa, I. Raşa, On the Hyers-Ulam stability of the linear differential equation, J. Math. Anal.Appl., 381(2011), 530-537.[9] D. Popa, I. Raşa, Hyers-Ulam stability of the linear differential operator with nonconstantcoefficients, Appl. Math. Comput., 219(2012), 1562-1568.[10] D. Popa, G. Pugna, I. Raşa, Bounds of solutions of some differential equations and Ulamstability, submitted.[11] I. Raşa, Entropies and Heun functions associated with positive linear operators, Appl. Math.Comput., 268 (2015), 422-431.[12] S.M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1960.
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Dorian Popa

Georgiana Pugna This is me

Ioan Rasa This is me

Publication Date June 30, 2018
Published in Issue Year 2018 Volume: 2 Issue: 2

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