Stability of delay differential equations in the sense of Ulam on unbounded intervals
[1] Ulam, S.M. (1960) A Collection of Mathe- matical Problems. Interscience, New York.
[2] Hyers, D. (1941) On the stability of the linear functional equation. Proceedings of National Academy of Sciences of the United States of America, 27(4), 222–224.
[3] Aoki, T. (1951) On the stability of the linear transformations in banach spaces. Bulletin of the American Mathematical Society, 57(1), 223–237.
[4] Bourgin, T.G. (1950) Classes of transforma- tions and bordering transformations. Journal of the Mathematical Society of Japan, 2(1), 64–66.
[5] Rassias, T. (1978) On the stability of linear mappings in Banach spaces. Proceedings of the American Mathematical Society, 72(1), 297–300.
[6] Popa, D. (2005) Hyers-Ulam-Rassias stability of a linear recurrence. Journal of Mathemat- ical Analysis and Applications, 309(2), 591– 597.
[7] Jung, S.M. (2001) Hyers-Ulam-Rassias Sta- bility of Functional Equations in Mathemati- cal Analysis. Hadronic Press, London.
[8] Rassias, T. (1953) Handbook of Functional Equations: Stability Theory. Springer, Lon- don.
[9] Cadariu, L., & Radu, V. (2008) Fixed point methods for the generalized stability of functional equations on a single variable. Fixed Point Theory and Applications, article ID749392, 15 pages.
[10] Forti, G.L. (2004) Comments on the core of the direct method for proving Hyers- Ulam stability of functional equations. Jour- nal of Mathematical Analysis and Applica- tions, 295(1), 127–133.
[11] Brzdek, J., Popa, D., & Xu, B. (2007) The Hyers-Ulam stability of nonlinear recurrences. Journal of Mathematical Analysis and Appli- cations, 335(1), 443–449.
[12] Petru, T.P., Petruel, A., & Yao, Y.C. (2011) Ulam-Hyers stability for operatorial equa- tions and inclusions via nonself operators.Taiwanese Journal of Mathematics, 15(5), 2195–2212.
[13] Obloza, M. (1993) Hyers-Ulam stability of the linear diferential equations. Rocznik Nauk-Dydakt Prace Matematik, 19(1), 259– 270.
[14] Obloza, M. (1997) Connections between Hy- ers and Lyapunov stability of the ordinary diferential equations. Rocznik Nauk-Dydakt Prace Matematik, 14(1), 141–146.
[15] Alsina, C., & Ger, R. (1998) On some in- equalities and stability results related to the exponential function. Journal of Inequalities and Applications, 2(1), 373–380.
[16] Miura, T., Takahasi, S.E., & Choda, H. (2001) On the Hyers-Ulam stability of real continuous function valued diferentiable map. Tokyo Journal of Mathematics, 24(2), 467–476.
[17] Miura, T. (2002) On the Hyers-Ulam stabil- ity of a diferentiable map. Japanese Journal of Mathematics, 55(1), 17–24.
[18] Takahasi, S.H., Miura, T., & Miyajima, S.(2002) The Hyers-Ulam stability constants of first order linear diferential operators. Bul- letin of Korean Mathematical Society, 39(1), 309–315.
[19] Jung, S.M. (2004) Hyers-Ulam stability of linear diferential equations of first order. Applied Mathematics Letters, 17(10), 1135– 1140.
[20] Miura, T., Miyajima, S., & Takahasi, S.H.(2003) A characterization of Hyers-Ulam sta- bility of first order linear diferential opera- tors. Journal of Mathematical Analysis and Applications, 286(1), 136–146.
[21] Takahasi, S.E., Takagi, H., Miura, T., & Miyajima, S. (2004) The Hyers-Ulam stabil- ity constants of first order linear diferential operators. Journal of Mathematical Analysis and Applications, 296(2), 403–409.
[22] Jung, S.M. (2006) Hyers-Ulam stability of linear diferential equations of first order. ii. Applied Mathematics Letters, 19(9), 854–858.
[23] Jung, S.M. (2005) Hyers-Ulam stability of linear diferential equations of first order. iii. Applied Mathematics Letters, 18(2), 139–146.
[24] Wang, G., Zhou, M., & Sun, L. (2008) Hyers- Ulam stability of linear diferential equations of first order. Applied Mathematics Letters, 21(10), 1024–1028.
[25] Jung, S.M., & Rassias, T.M. (2008) Gener- alized Hyers-Ulam stability of riccati difer- ential equation. Mathematical Inequalities & Applications, 11(4), 777–782.
[26] Rus, I.A. (2009) Ulam stability of ordi- nary diferential equations. Studia Universi- tatis Babe-Bolyai Mathematica, 54(4), 297– 300.
[27] Rus, I.A. (2010) Ulam stabilities of ordi- nary diferential equations in a Banach space. Carpathian Journal of Mathematics, 26(1), 103–107.
[28] Jung, S.M. (2010) A fixed point approach to the stability of diferential equations y′ = f(x, y). Bulletin of the Malaysian Mathemat- ical Sciences Society, 33(1), 47–56.
[29] Li, X & Wang, J. (2013) Ulam-Hyers-Rassias stability of semilinear diferential equations with impulses. Electronic Journal of Difer- ential Equations, 2013(172), 1–8.
[30] Qarawani, M.N. (2014) On Hyers-Ulam- Rassias stability for bernoulli’s and first order linear and nonlinear diferential equations. British Journal of Mathematics and Com- puter Science, 4(11), 1615–1628.
[31] Alqifiary, Q.H. (2014) Note on the stability for linear systems of diferential equations. In- ternational Journal of Applied Mathematical Research, 3(1), 15–22.
[32] Onitsuka, M., & Shoji, T. (2017) Hyers-ulam stability of first-order homogeneous lineardif- ferential equations with a real-valued coef- ficient. Applied Mathematics Letters, 63(1), 102–108.
[33] Jung, S.M., & Brzdek, J. (2010) Hyers- Ulam stability of the delay equation y′ (t) = λy (t − τ). Abstract and Applied Analysis, 2010(3), 10 pages.
[34] Otrocol, D., & Ilea, V. (2013) Ulam stability for a delay diferential equation. Central Eu- ropean Journal of Mathematics, 11(7), 1296– 1303.
[35] Tun, C., & Bier, E. (2015) Hyers-Ulam- Rassias stability for a first order functional diferential equation. Journal of Mathemat- ical and Fundamental Sciences, 47(2), 143– 153.
[36] Andr/as, S., & M/esz/aros, A.R. (2013) Ulam- Hyers stability of dynamic equations on time scales via Picard operators. Applied Mathe- matics and Computation, 219(4), 4853–4864.
[37] Shen, Y. (2017) The Ulam stability of first or- der linear dynamic equations on time scales. Results in Mathematics, Online first.
[38] Zada, A., Shah, S.O., Ismail, S., & Li, T.(2017) Hyers-Ulam stability in terms of di- chotomy of first order linear dynamic system. Punjab University Journal of Mathematics, 49(3), 37-47.
[39] Trigeassou, J.C., Maamri, N., Sabatier, J., & Oustaloupa, A. (2011) A Lyapunov approach to the stability of fractional diferential equa- tions. Signal Processing, 91(3), 437–445.
[40] Li, C.P., & Zhang, F.R. (2011) A survey on the stability of fractional diferential equa- tions. The European Physical Journal Special Topics, 193(1), 27–47.
[41] Bayram, M,. Seer, A., & Adgzel, H. (2017) Oscillatory behavior of solutions of diferen- tial equations with fractional order. Applied Mathematics & Information Sciences, 11(3), 683–691.
[42] Bayram, M., Adgzel, H., & Seer, A. (2016) Oscillation criteria for nonlinear fractional diferential equation with damping term. Open Physics, 14(1), 119–128.
[43] Seer, A., & Adgzel, H. (2016) Oscillation of solutions for a class of nonlinear fractional dif- ference equations. The Journal of Nonlinear Science and Applications, 9(11), 5862–5869.
[44] Miura, T., Miyajima, S., & Takahasi, S.H.(2003) Hyers-Ulam stability of linear diferen- tial operator with constant coe伍cients. Math- ematische Nachrichten, 258(2), 90–96.