Central European Journal of Mathematics

, Volume 11, Issue 7, pp 1296–1303 | Cite as

Ulam stability for a delay differential equation

Research Article

Abstract

We study the Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability for a delay differential equation. Some examples are given.

Keywords

Ulam-Hyers stability Ulam-Hyers-Rassias stability Delay differential equation 

MSC

34K20 34L05 47H10 

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References

  1. [1]
    Bota-Boriceanu M.F., Petruşel A., Ulam-Hyers stability for operatorial equations, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 2011, 57(suppl. 1), 65–74MATHGoogle Scholar
  2. [2]
    Castro L.P., Ramos A., Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations, Banach J. Math. Anal., 2009, 3(1), 36–43MathSciNetGoogle Scholar
  3. [3]
    Guo D., Lakshmikantham V., Liu X., Nonlinear Integral Equations in Abstract Spaces, Math. Appl., 373, Kuwer, Dordrecht, 1996MATHGoogle Scholar
  4. [4]
    Hyers D.H., Isac G., Rassias Th.M., Stability of Functional Equations in Several Variables, Progr. Nonlinear Differential Equations Appl., 34, Birkhäuser, Boston, 1998MATHCrossRefGoogle Scholar
  5. [5]
    Jung S.-M., A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl., 2007, #57064Google Scholar
  6. [6]
    Kolmanovskiĭ V., Myshkis A., Applied Theory of Functional-Differential Equations, Math. Appl. (Soviet Ser.), 85, Kluwer, Dordrecht, 1992CrossRefGoogle Scholar
  7. [7]
    Otrocol D., Ulam stabilities of differential equation with abstract Volterra operator in a Banach space, Nonlinear Funct. Anal. Appl., 2010, 15(4), 613–619MathSciNetMATHGoogle Scholar
  8. [8]
    Petru T.P., Petruşel A., Yao J.-C., Ulam-Hyers stability for operatorial equations and inclusions via nonself operators, Taiwanese J. Math., 2011, 15(5), 2195–2212Google Scholar
  9. [9]
    Radu V., The fixed point alternative and the stability of functional equations, Fixed Point Theory, 2003, 4(1), 91–96MathSciNetMATHGoogle Scholar
  10. [10]
    Rassias Th.M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 1978, 72(2), 297–300MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    Rus I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001MATHGoogle Scholar
  12. [12]
    Rus I.A., Gronwall lemmas: ten open problems, Sci. Math. Jpn., 2009, 70(2), 221–228MathSciNetMATHGoogle Scholar
  13. [13]
    Rus I.A., Ulam stability of ordinary differential equations, Stud. Univ. Babeş-Bolyai Math., 2009, 54(4), 125–133MathSciNetMATHGoogle Scholar
  14. [14]
    Rus I.A., Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 2009, 10(2), 305–320MathSciNetMATHGoogle Scholar
  15. [15]
    Ulam S.M., A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, 8, Interscience, New York-London, 1960MATHGoogle Scholar

Copyright information

© Versita Warsaw and Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.“T. Popoviciu” Institute of Numerical AnalysisRomanian AcademyCluj-NapocaRomania
  2. 2.Department of Mathematics, Faculty of Mathematics and Computer Science“Babeş-Bolyai” UniversityCluj-NapocaRomania

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