Ulam stability for a delay differential equation

• Autorzy: Diana Otrocol , Veronica Ilea
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

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

Kategorie tematyczne

• 34K20: Stability theory
• 47H10: Fixed-point theorems
• 34L05: General spectral theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 7
• Strony: 1296-1303

Daty

wydano

2013-07-01

online

2013-04-26

Twórcy

autor

Diana Otrocol

• “T. Popoviciu” Institute of Numerical Analysis, Romanian Academy, Fântânele 57, Cluj-Napoca, 400320, Romania

autor

Veronica Ilea

• Department of Mathematics, Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, M. Kogălniceanu 1, Cluj-Napoca, 400084, Romania

Bibliografia

• [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
• [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 http://dx.doi.org/10.1007/978-1-4612-1790-9[Crossref]
• [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]
• [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., Petruşel 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 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
• [13] Rus I.A., Ulam stability of ordinary differential equations, Stud. Univ. Babeş-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

Identyfikatory

DOI

10.2478/s11533-013-0233-9