Ulam stability for a delay differential equation
Diana Otrocol ; Veronica Ilea
Open Mathematics, Tome 11 (2013), p. 1296-1303 / Harvested from The Polish Digital Mathematics Library
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We study the Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability for a delay differential equation. Some examples are given.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:269304 
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     author = {Diana Otrocol and Veronica Ilea},
     title = {Ulam stability for a delay differential equation},
     journal = {Open Mathematics},
     volume = {11},
     year = {2013},
     pages = {1296-1303},
     zbl = {1275.34098},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0233-9}
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Diana Otrocol; Veronica Ilea. Ulam stability for a delay differential equation. Open Mathematics, Tome 11 (2013) pp. 1296-1303. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0233-9/

[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 | Zbl 1265.54158

[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 | Zbl 1177.45010

[3] Guo D., Lakshmikantham V., Liu X., Nonlinear Integral Equations in Abstract Spaces, Math. Appl., 373, Kuwer, Dordrecht, 1996 | Zbl 0866.45004

[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/10.1007/978-1-4612-1790-9[Crossref] | Zbl 0907.39025

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

[6] Kolmanovskiĭ V., Myshkis A., Applied Theory of Functional-Differential Equations, Math. Appl. (Soviet Ser.), 85, Kluwer, Dordrecht, 1992 http://dx.doi.org/10.1007/978-94-015-8084-7[Crossref] | Zbl 0917.34001

[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 | Zbl 1242.45011

[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 | Zbl 1246.54049

[9] Radu V., The fixed point alternative and the stability of functional equations, Fixed Point Theory, 2003, 4(1), 91–96 | Zbl 1051.39031

[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/S0002-9939-1978-0507327-1[Crossref]

[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 | Zbl 1223.47064

[13] Rus I.A., Ulam stability of ordinary differential equations, Stud. Univ. Babeş-Bolyai Math., 2009, 54(4), 125–133 | Zbl 1224.34165

[14] Rus I.A., Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 2009, 10(2), 305–320 | Zbl 1204.47071

[15] Ulam S.M., A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, 8, Interscience, New York-London, 1960 | Zbl 0086.24101