Abstract
We study the Ulam–Hyers stability and generalized Ulam–Hyers–Rassias stability for a delay differential equation. Some examples are given.
Authors
D. Otrocol
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
V.A. Ilea
(Babes Bolyai Univ.)
Keywords
Cite this paper as:
D. Otrocol, V. Ilea, Ulam stability for a delay differential equation, Cent. Eur. J. Math., Vol. 11(7) (2013), pp. 1296-1303, doi: 10.2478/s11533-013-0233-9
About this paper
Journal
Central European Journal of Mathematics
Publisher Name
Versita, Warsaw, Poland
Print ISSN
1895-1074
Online ISSN
MR
MR3047057
ZBL
Google Scholar
[1] Bota-Boriceanu M.F., Petrușel A., Ulam–Hyers stability for operatorial equations, An. Știinţ. Univ. Al.I. Cuza Iași. Mat. (N.S.), 2011, 57(suppl. 1), 65–74
[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), 36–43
[3] Guo D., Lakshmikantham V., Liu X., Nonlinear Integral Equations in Abstract Spaces, Math. Appl., 373, Kuwer, Dordrecht, 1996
[4] Hyers D.H., Isac G., Rassias Th.M., Stability of Functional Equations in Several Variables, Progr. Nonlinear Differential Equations Appl., 34, Birkhäuser, Boston, 1998
[5] Jung S.-M., A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl., 2007, # 57064
[6] Kolmanovskiı V., Myshkis A., Applied Theory of Functional-Differential Equations, Math. Appl. (Soviet Ser.), 85, Kluwer, Dordrecht, 1992
[7] Otrocol D., Ulam stabilities of differential equation with abstract Volterra operator in a Banach space, Nonlinear Funct. Anal. Appl., 2010, 15(4), 613–619
[8] Petru T.P., Petrușel A., Yao J.-C., Ulam–Hyers stability for operatorial equations and inclusions via nonself operators, Taiwanese J. Math., 2011, 15(5), 2195–2212
[9] Radu V., The fixed point alternative and the stability of functional equations, Fixed Point Theory, 2003, 4(1), 91–96
[10] Rassias Th.M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 1978, 72(2), 297–300
[11] Rus I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001
[12] Rus I.A., Gronwall lemmas: ten open problems, Sci. Math. Jpn., 2009, 70(2), 221–228
[13] Rus I.A., Ulam stability of ordinary differential equations, Stud. Univ. Babeș-Bolyai Math., 2009, 54(4), 125–133
[14] Rus I.A., Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 2009, 10(2), 305–320
[15] Ulam S.M., A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, 8, Interscience, New York–London, 1960