Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 26, 2013

Ulam stability for a delay differential equation

  • Diana Otrocol EMAIL logo and Veronica Ilea
From the journal Open Mathematics

Abstract

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

[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), 65–74 10.2478/v10157-011-0003-6Search in Google Scholar

[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 10.15352/bjma/1240336421Search in Google Scholar

[3] Guo D., Lakshmikantham V., Liu X., Nonlinear Integral Equations in Abstract Spaces, Math. Appl., 373, Kuwer, Dordrecht, 1996 10.1007/978-1-4613-1281-9Search in Google Scholar

[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 http://dx.doi.org/10.1007/978-1-4612-1790-910.1007/978-1-4612-1790-9Search in Google Scholar

[5] Jung S.-M., A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl., 2007, #57064 10.1155/2007/57064Search in Google Scholar

[6] Kolmanovskiĭ V., Myshkis A., Applied Theory of Functional-Differential Equations, Math. Appl. (Soviet Ser.), 85, Kluwer, Dordrecht, 1992 http://dx.doi.org/10.1007/978-94-015-8084-710.1007/978-94-015-8084-7Search in Google Scholar

[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 Search in Google Scholar

[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), 2195–2212 10.11650/twjm/1500406430Search in Google Scholar

[9] Radu V., The fixed point alternative and the stability of functional equations, Fixed Point Theory, 2003, 4(1), 91–96 Search in Google Scholar

[10] Rassias Th.M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 1978, 72(2), 297–300 http://dx.doi.org/10.1090/S0002-9939-1978-0507327-110.1090/S0002-9939-1978-0507327-1Search in Google Scholar

[11] Rus I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001 Search in Google Scholar

[12] Rus I.A., Gronwall lemmas: ten open problems, Sci. Math. Jpn., 2009, 70(2), 221–228 Search in Google Scholar

[13] Rus I.A., Ulam stability of ordinary differential equations, Stud. Univ. Babeş-Bolyai Math., 2009, 54(4), 125–133 Search in Google Scholar

[14] Rus I.A., Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 2009, 10(2), 305–320 Search in Google Scholar

[15] Ulam S.M., A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, 8, Interscience, New York-London, 1960 Search in Google Scholar

Published Online: 2013-4-26
Published in Print: 2013-7-1

© 2013 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 24.4.2024 from https://www.degruyter.com/document/doi/10.2478/s11533-013-0233-9/html
Scroll to top button