International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

On Hyers-Ulam Stability for Nonlinear Differential Equations of nth Order

  • Maher Nazmi Qarawani1
  1. Al-quds Open University

Abstract

This paper considers the stability of nonlinear differential equations of nth order in the sense of Hyers and Ulam. It also considers the Hyers-Ulam stability for superlinear Emden-Fowler differential equation of nth order. Some illustrative examples are given.

How to Cite

M. N. Qarawani, On Hyers-Ulam Stability for Nonlinear Differential Equations of nth Order, Int. J. Anal. Appl. 2 (2013), 71–78.

BibTeX
@article{Qarawani2013,
  author  = {Qarawani, Maher Nazmi},
  title   = {On Hyers-Ulam Stability for Nonlinear Differential Equations of nth Order},
  journal = {Int. J. Anal. Appl.},
  volume  = {2},
  year    = {2013},
  pages   = {71--78},
  doi     = {}
}

References

  • [1] Ulam S.M., (1964), Problems in Modern Mathematics, John Wiley & Sons, New York, NY, USA, Science edition.
  • [2] Hyers D. H., (1941), On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222-224.
  • [3] Rassias T. M. (1978), On the stability of the linear mapping in Banach spaces, Proceedings of the American Mathemaical Society, vol. 72, no. 2, pp. 297-300.
  • [4] Miura T., Takahasi S.-E., Choda H., (2001), On the Hyers-Ulam stability of real continuous function valued differentiable map, Tokyo Journal of Mathematics 24, pp. 467-476.
  • [5] Jung S. M., (1996), On the Hyers-Ulam-Rassias stability of approximately addi- tive mappings, Journal of Mathematics Analysis and Application 204, pp. 221-226.
  • [6] Park C. G., (2002), On the stability of the linear mapping in Banach modules,Journal of Mathematics Analysis and Application 275, pp. 711-720.
  • [7] Gavruta P., (1994), A generalization of t he Hyers-Ulam-Rassias stability of approximately additive mappings, Journal of Mathematical Analysis and Applications, vol. 184, no. 3 , pp. 431-436.
  • [8] Jun K .-W., Lee Y. -H., (2004), A generalization of the Hyers-Ulam-Rassias stability of the Pexiderized quadratice quations, Journal of Mathematcal Analysis and Applications , vol. 297, no. 1, pp. 70- 86.
  • [9] Jung S.-M. (2001), Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, Fla, U SA.
  • [10] Park C. , (2005), Homomorphisms between Poisson JC*-algebras, Bulletin of the Brazilian Mathematical Society, vol. 36, no. 1 , pp. 79-97.
  • [11] C. Park, Cho Y.-S. and Han M., (2007), Functional inequalities associated with Jordan-von Neumanntype additive functional equations, Journal of Inequalities and Applications , vol. 2007, Article ID 41820, 13 pages.
  • [12] Alsina C., Ger R., (1998), On some inequalities and stability results related to the exponential function, Journal of Inequalities and Application 2, pp 373-380.
  • [13] Takahasi E., Miura T., and Miyajima S., (2002), On the Hyers-Ulam stability of the Banach space-valued differential equation y 0 = λy, Bulletin of the Korean Mathematical Society, vol. 39, no. 2, pp 309-315.
  • [14] Miura T., Miyajima S., Takahasi S.-E., (2007), A characterization of Hyers-Ulam stability of first order linear differential operators, Journal of Mathematics Analysis and Application 286. pp. 136-146.
  • [15] Jung S. M., (2005), Hyers-Ulam stability of linear differential equations of first order, Journal of Mathematics Analysis and Application 311, pp. 139-146.
  • [16] Wang G., Zhou M. and Sun L. (2008), Hyers-Ulam stability of linear differential equations of first order, Applied Mathematics Letters 21, pp 1024-1028.
  • [17] Li Y., (2010), Hyers-Ulam Stability of Linear Differential Equations,Thai Journal of Mathematics,Vol. 8 No 2, pp 215-219.
  • [18] Li Y. and Shen Y., (2009), Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order, International Journal of Mathematics and Mathematical Sciences, Vol. 2009, Article ID 576852, pp. 7.
  • [19] Gavruta P., Jung S. and Li Y. , (2011), Hyers-Ulam Stability For Second-Order Linear Differential Equations With Boundary Conditions, EJDE, Vol.2011, No. 80, pp1-7, .http://ejde.math.txstate.edu/Volumes/2011/80/gavruta.pdf.
  • [20] Qarawani M. N., (2012), Hyers-Ulam Stability of a Generalized Second- Order Nonlinear Differential Equation, Applied Mathematics,Vol. 3, No. 12, pp. 1857-1861. doi: 10.4236/am.2012.312252.