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IJAMR International Journal of Applied Mathematical Research E-ISSN 2227-4324

Hyers-Ulam Stability of Linear and Nonlinear Differential Equations of Second Order

Authors and Affiliations

  • Maher Nazmi Qarawani Alquds Open University

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Abstract

In this paper we established the Hyers-Ulam stability of a nonlinear differential equation of second order with initial condition. We also proved the Hyers -Ulam stability of a linear differential equation of second order with initial condition.

Author Biography

  • Maher Nazmi Qarawani, Alquds Open University
    Head of Department of Mathematics

References

[1] S.-M. Ulam, Problems in Modern Mathematics , Science Edition, John Wiley & Sons, New York, USA, 1964.

[2] D. H . Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America, 27 (1941) 222–224.

[3] T. M . Rassias, On the stability of the linear mapping in Banach spaces, Proceedings of the American Mathematical Society, 72 (2) (1978) 297–300.

[4] T. Miura, S.-E. Takahasi, H. Choda, On the Hyers-Ulam stability of real continuous function valued differentiable map, Tokyo J. Math. 24 (2001) 467–476.

[5] S. M. Jung, On the Hyers-Ulam-Rassias stability of approximately additive- mappings, J. Math. Anal. Appl. 204 (1996) 221-226.

View more references (15)

[6] C. G. Park, On the stability of the linear mapping in Banach modules , J. Math. Anal. Appl. 275 (2002) 711-720.

[7] C. Alsina, R. Ger, On some inequalities and stability results related to the exponential function, J. Inequal Appl. 2 (4) (1998) 373-380.

[8] E. Takahasi , T. Miura, S. Miyajima, On the Hyers-Ulam stability of the Banach space-valued differential equation y′ = λy , Bulletin of the Korean Mathematical Society 39(2002) 309–315.

[9] T. Miura, S. Miyajima, S.-E. Takahasi, A characterization of Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl. 286 (2003) 136-146.

432 Maher Qarawani

[10] G. Wang, M. Zhou, L. Sun, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett. 21(2008) 1024-1028.

[11] S.-M. Jung, Hyers-Ulam stability of linear differential equations of first order, J. Math. Anal. Appl. 311(2005) 139-146.

[12] S.-M. Jung, Legendre’s differential equation and Its Hyers-Ulam stability, Abstract and Applied Analysis (2007) doi:10.1155/2007/56419.

[13] Y. Li, Hyers-Ulam Stability of Linear Differential Equations, Thai Journal of Mathematics 8 (2) (2010) 215–219.

[14] P. Gavruta, S. Jung, Y. Li, Hyers-Ulam Stability For SecondOrder Linear Differential Equations With Boundary Conditions, EJDE

http://ejde.math.txstate.edu/Volumes/2011/80/gavruta.pdf

[15] Y. Li and Y. Shen, Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order, Int. J. Math. Math. Sci. (2009) doi:10.1155/2009/576852.

[16] A. Javadian, E. Sorouri, G. Kim, M. E. Gordji, Generalized Hyers-Ulam stability of the second-order linear differential equations, J of Applied Mathematics (2011) doi:10.1155/2011/813137.

[17] M. N. Qarawani, Boundedness and asymptotic behaviour of solutions of a second order nonlinear differential equation, J. of Mathematics Research 4(3) (2012) 121-128.

[18] A. Bucur, About asymptotic behaviour of solutions of differential equations as x → ∞,General Mathematics 14 (2) (2006) 55-58.


How to Cite

Qarawani, M. N. (2012). Hyers-Ulam Stability of Linear and Nonlinear Differential Equations of Second Order. International Journal of Applied Mathematical Research, 1(4), 422-432. https://doi.org/10.14419/ijamr.v1i4.160