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Abstract

For the first time in 1933, Abloza studied the stability of Hyers-Ulam linear differential equations. Since then, many articles have been published in this field, some of which can be found in references (6-19). In this paper, we investigate the stability of linear differential equations in a non-Archimedean normed space. Let (R,∥⋅∥)(R, \|\cdot\|)(R,∥⋅∥) be a non-Archimedean normed space of real numbers. In this paper, we prove the Hyers-Ulam stability of nonhomogeneous second-order linear differential equations with non-constant coefficients, y′′+f(x)y′+g(x)y=h(x)y'' + f(x)y' + g(x)y = h(x)y′′+f(x)y′+g(x)y=h(x), in the non-Archimedean normed space (R,∥⋅∥)(R, \|\cdot\|)(R,∥⋅∥), where f,g,h:(a,b)⊆R→Rf, g, h : (a, b) \subseteq \mathbb{R} \rightarrow \mathbb{R}f,g,h:(a,b)⊆R→R are given continuous functions.

Keywords

Hyers-Ulam Stability Linear Differential Equations Non-Archimedean Norm Norm Normed Space

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Stori, M. K. (2025). Non-Archimedean Stability of Nonhomogeneous Second-Order Linear Differential Equation. Journal of Natural Sciences – Kabul University, 3(3), 235–244. https://doi.org/10.62810/jns.v3i3.185
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References

  1. Czerwik, S. Functional Equations and Inequalities in several variables, (2002). World scientific, Singapore.
  2. Hyers, D.H., Isac, G. and Rassias, T.M. stability of Functional Equation in Several Variables, (1998). Birkhauser, boston.
  3. Sahoo. P. K and kannappan, P. Introduction to Functional Equations, (2011). CRC press, boca Raton.
  4. Obloza, M. Hyers stability of the linear differential equations, (1993). Rocz.nauk. – Dydakt.Pr.Mat .13,259-270.
  5. Obloza, M. connection between Hyers and Lyapunov stability of the ordinary differential equation, (1997). Rocz.nauk. -Dyadakt.Pr. Mat. 14,141-146.
  6. Alsina, C and Ger, R. On some inequalities and stability results related to the exponential function, (1998). J.inequal.Appl.2,373-380.
  7. Gavruta, P, Jung, S-M. and Li, Y. Hyers-Ulem stability for second- order linear differential equation with Electronic. (2011). J. Differ.Equ,.801-805.
  8. jung, S-M. Hyers –Ulam stability of linear differential equation of first order, (2004). Appl. Math. Lett. 17, 1135-1140.
  9. Jung, S-M. Hyers –Ulam stability of linear differential equation of first order, II, (2006). Appl. Math. Lett. 19, 854-140.
  10. Jung, S-M. Hyers. Ulam stability of a system of first order linear differential equation with constant coefficients, (2006). J. Math. Anal. Apple. 320,549-561.
  11. Miura, T.,Oka ,H,.Talahasi, S-E.and Niwa , N. Hyers –Ulam stability of first order linear differential equation for banach space-valued holomorphic mappings, (2007). J. Math. in equal. 3 ,377-385.
  12. popa, D. Rasa, I. On the Hyers-Ulam of the linear differential equation, (2011). J. Math. Anal. Appl. 381, 530 537.
  13. popa, D. Rasa, I. On the Hyers-Ulam of the linear differential operator with non – constant coefficient, (2011). Appl. Math. Compute. 219, 1562- 1568.
  14. Rus, I, A. Ulam stability of ordinary differential equation, stud. (2009).Univ. Babes-Bolyai, Math.54, 125-134.
  15. Wang, G.,Zhou, M .and Sun , L. Hyers-Ulam stability of differential. equation of first order, (2008). Appl, Math. Lett. 21, 1024-1028.
  16. Alqifary, Q.H. and Jung, S-M. On the hyers –Ulam stability of differential equation of second order, (2014). Abstr. Appl. Anal., Article ID 483707.
  17. Cimpean, D.S. and popa, On the stability of the linear differential equation of higher order with constant coefficient, (2010). Appl. Math. Compute. 217,4141-4146.
  18. Ghamei, M.B., Gordji, M.E., Alizadeh and B, Park, C. Hyers – Ulam stability of exact second –order linear differential equation, Adv. (2012). Differ. Equ., Article ID 36.
  19. Li, Y. and shen, Y. Hyers -Ulam stability of linear differential. equation of second order, (2010). Appl. Math. 23, 306-309.