On Ulam stability of the second order linear differential equation

Yıl 2018, Cilt: 2 Sayı: 2, 106 - 112, 30.06.2018

Dorian Popa , Georgiana Pugna Ioan Rasa

https://doi.org/10.31197/atnaa.402721

Cited By: 1

Öz

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.

Anahtar Kelimeler

Ulam stability, Banach spaces, Heun Equation

Kaynakça

• [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.