Asymptotic stability of nonlinear neutral delay integro-differential equations

References

[1] Ambrossetti, A.: Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Mat. Univ. Padova 39 (1967), 349–360.Search in Google Scholar

[2] Ardjouni, A.—Djoudi, A.: Fixed points and stability in linear neutral differential equations with variable delays, Nonlinear Anal. 74 (2011), 2062–2070.10.1016/j.na.2010.10.050Search in Google Scholar

[3] Ardjouni, A.—Djoudi, A.: Stability in nonlinear neutral differential with variable delays using fixed point theory, Electron. J. Qual. Theory Differ. Equ. 2011 (2011), Art. No. 43.10.14232/ejqtde.2011.1.43Search in Google Scholar

[4] Ardjouni, A.—Djoudi, A.: Fixed points and stability in linear neutral differential equations with variable delays, Opuscula Math. 32(1) (2012), 5–9.Search in Google Scholar

[5] Ardjouni, A.—Djoudi, A.—Soualhia, I.: Stability for linear neutral integro-differential equations with variable delays, Electron. J. Qual. Theory Differ. Equ. 2012 (2012), Art. No. 172.10.7494/OpMath.2012.32.1.5Search in Google Scholar

[6] Boe, E.—Chang, H. C.: Dynamics of delayed systems under feedback control, Chem. Engng. Sci. 44 (1989), 1281–1294.10.1016/0009-2509(89)85002-XSearch in Google Scholar

[7] Brayton, R. K.—Willoughby, R. A.: On the numerical integration of a symmetric system of difference-differential equations of Neutral type, J. Math. Anal. Appl. 18 (1976), 182–189.10.1016/0022-247X(67)90191-6Search in Google Scholar

[8] Banaś, J.—Goebel, K.: Measures of Noncompactness in Banach Spaces. Lecture Notes in Pure Appl. Math. 60, Mercel Dekker, New York and Basel, 1980.Search in Google Scholar

[9] Becker, L. C.—Burton, T. A.: Stability, fixed points and inverse of delay, Proc. Roy. Soc. Edinb. A 136 (2006), 245–275.10.1017/S0308210500004546Search in Google Scholar

[10] Burton, T. A.: Fixed points and stability of nonconvolution equation, Proc. Amer. Math. Soc. 132 (2004), 3679–3687.10.1090/S0002-9939-04-07497-0Search in Google Scholar

[11] Burton, T. A.: Stability for Fixed Point Theory for Functional Differential Equations, Dover Publications, New York, 2006.Search in Google Scholar

[12] Burton, T. A.: Liapunov functionals, fixed points, and stability by Krasnoselskii's theorem, Nonlinear Stud. 9 (2001), 181–190.Search in Google Scholar

[13] Burton, T. A.: Stability by fixed point theory or Lyapunov theory: A comparison, Fixed Point Theory 4 (2003), 15–32.Search in Google Scholar

[14] Burton, T. A.—Furumochi, T.: A note on stability by Schauder's theorem, Funkcial. Ekvac. 44 (2001), 73–82.Search in Google Scholar

[15] Burton, T. A.—Furumochi, T.: Fixed points and problems in stability theory, Dyn. Sys. Appl. 10 (2001), 89–116.Search in Google Scholar

[16] Burton, T. A.—Furumochi, T.: Asymptotic behavior of solutions of functional differential equations by fixed point theorems, Dyn. Sys. Appl. 11 (2002), 499–519.Search in Google Scholar

[17] Burton, T. A.—Furumochi, T.: Krasnosielskii's fixed point theorem and stability, Nonlinear Anal. 49 (2002), 445–454.10.1016/S0362-546X(01)00111-0Search in Google Scholar

[18] Dib, Y. M.—Maroun, M. R.—Raffoul, Y. N.: Periodicity and stability in neutral nonlinear differential equations with functional delay, Electron. J. Qual. Theory Differ. Equ. 2005 (2005), Art. No. 142.Search in Google Scholar

[19] Djoudi, A.—Khemis, R.: Fixed point techniques and stability for neutral nonlinear differential equations with unbounded delays, Georgian Math. J. 13 (2006), 25–34.10.1515/GMJ.2006.25Search in Google Scholar

[20] Driver, D. R.: A mixed neutral systems, Nonlinear Anal. 8 (1984), 155-158.10.1016/0362-546X(84)90066-XSearch in Google Scholar

[21] Jin, C. H.—Luo, J. W.: Stability of an integro-differential equation, Comp. Math. Appl. 57 (2009), 1080–1088.10.1016/j.camwa.2009.01.006Search in Google Scholar

[22] Jin, C. H.—Luo, J. W.: Stability in functional differential equations established using fixed point theory, Nonlinear Anal. 68 (2008), 3307–3315.10.1016/j.na.2007.03.017Search in Google Scholar

[23] Jin, C. H.—Luo, J. W.: Fixed points and stability in neutral differential equations with variable delays, Proc. Amer. Math. Soc. 136 (2008), 909–918.10.1090/S0002-9939-07-09089-2Search in Google Scholar

[24] Hale, J. K.: Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.10.1007/978-1-4612-9892-2Search in Google Scholar

[25] Popov, E. P.: Automatic Regulation and Control, Nauka, Moscow, 1966 (in Russian).Search in Google Scholar

[26] Raffoul, Y. N.: Stability in neutral nonlinear differential equations with functional delays using fixed point theory, Math. Comput. Modelling 40 (2004), 691–700.10.1016/j.mcm.2004.10.001Search in Google Scholar

[27] Sadovskii, B. N.: Limit-compact and condensing operators, Russian Math. Surveys 27 (1972), 86–144.10.1070/RM1972v027n01ABEH001364Search in Google Scholar