References
- V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noord-hoff, Leyden, 1976.
- J. Dyson and R. V. Bressan, Functional differential equations and non-linear evolution operators, Proc. Roy. Soc. Edinburgh Ser. A 75 (1975/1976), no. 3, 223-234. https://doi.org/10.1017/S0308210500017959
- J. Dyson and R. V. Bressan, Semigroups of translations associated with functional and functional-differential equations, Proc. Roy. Soc. Edinburgh Sect. A 82 (1978/79), no. 3-4, 171-188. https://doi.org/10.1017/S030821050001115X
- Z. Fan, Existence and continuous dependence results for nonlinear differential inclusions with infinite delay, Nonlinear Anal. 69 (2008), no. 8, 2379-2392. https://doi.org/10.1016/j.na.2007.08.011
- W. Fitzgibbon, Representation and approximation of solutions to semilinear Volterra equations with delay, J. Differential Equations 32 (1979), no. 2, 233-249. https://doi.org/10.1016/0022-0396(79)90060-3
- C. Gori, V. Obukhovskii, M. Ragni, and P. Rubbioni, Existence and continuous dependence results for semilinear functional differential inclusions with infinite delay, Nonlinear Anal. 51 (2002), 765-782. https://doi.org/10.1016/S0362-546X(01)00861-6
- J. K. Hale and J. Kato, Phace space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), no. 1, 11-41.
- H. R. Henriquez, Differentiability of solutions of second-order functional differential equations with unbounded delay, J. Math. Anal. Appl. 280 (2003), no. 2, 284-312. https://doi.org/10.1016/S0022-247X(03)00042-8
- Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Infinite Delay, in Lecture Notes in Math. Vol. 1473, Springer-Verlag, Berlin, 1991.
- A. G. Kartsatos and M. E. Parrott Convergence of the Kato approximants for evolution equations involving functional perturbations, J. Differential Equations 47 (1983), no. 3, 358-377. https://doi.org/10.1016/0022-0396(83)90041-4
- T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508-520. https://doi.org/10.2969/jmsj/01940508
- J. Liang and T. J. Xiao, The Cauchy problem for nonlinear abstract functional differential equations with infinite delay, Comput. Math. Appl. 40 (2000), no. 6-7, 693-703. https://doi.org/10.1016/S0898-1221(00)00188-7
- N. H. Pavel, Nonlinear evolution operators and semigroups, in Lecture Notes in Mathematics, Vol. 1260, Springer-Verlag, Berlin, 1987.
- K. Schumacher, Existence and continuous dependence for functional differential equations with unbounded delay, Arch. Ration. Mech. Anal. 67 (1978), no. 4, 315-335.
- C. C. Travis and G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395-418. https://doi.org/10.1090/S0002-9947-1974-0382808-3
-
C. C. Travis and G. F. Webb, Existence, stability and compactness in the
${\alpha}$ -norm for partial functional differential equations, Trans. Amer. Math. Soc. 240 (1978), 129-143. - G. F. Webb, Autonomous nonlinear functional differential equations and nonlinear semigroups, J. Math. Anal. Appl. 46 (1974), 1-12. https://doi.org/10.1016/0022-247X(74)90277-7
- G. F. Webb, Asymptotic stability for abstract nonlinear functional differential equations, Proc. Amer. Math. Soc. 54 (1976), 225-230. https://doi.org/10.1090/S0002-9939-1976-0402237-0
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