Abstract
In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.
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Atkinson F V and Haddock J R, On determining phase spaces for functional differential equations, Funkcialaj Ekvacioj 31 (1988) 331–347
Burger R, An integro-differential equation from population genetics and perturbations of differentiable semigroups in Frechet spaces, Proc. R. Soc. Edin. 118A (1991) 63–73
Choe Y H, C 0-semigroups on a locally convex space, J. Math. Anal. Appl. 106 (1985) 293–320
de Laubenfels R, Existence families, functional calculi and evolution equations, LNM 1570 (Springer Verlag) (1994)
Haddock J R, Nkashama M N and Wu J, Asymptotic constancy for linear neutral Volterra integrodifferential equations, Tohuku Math. J. 41 (1989) 689–710
Haddock J and Terjeki J, On the location of positive limit sets for autonomous functional differential equations with infinite delay, J. Diff. Eqns 86 (1990) 1–31
Hale J K and Verduyn Lunel M, Introduction to functional differential equations (New York: Springer Verlag) (1993)
Hale J K and Kato J, Phase spaces for retarded equations with infinite delay, Funkcial Ekvac. 21 (1978) 11–41
Hamilton R, The inverse function theorem of Nash and Moser, Bull. Am. Math. Soc. 7 (1982) 1–64
Kantorovitz S, The Hille-Yosida space of an arbitrary operator, J. Math. Anal. Appl. 136 (1988) 107–111
Komura T, Semigroups of operators in locally convex spaces, J. Funct. Anal. 2 (1968) 258–296
Lobanov S G and Smolyanov O G, Ordinary differential equations in locally convex spaces, Usp. Mat. Nauk. 49 (1994) 93–168
Oharu S, Semilinear evolution equations in Frechet spaces, Differential equations in Banach spaces (Springer Verlag) LNM 1223 (1986) pp. 186–207
Rudin W, Functional Analysis (New Delhi: TMH) (1974)
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Sengadir, T. Semigroups on Frechet spaces and equations with infinite delays. Proc Math Sci 117, 71–84 (2007). https://doi.org/10.1007/s12044-007-0006-0
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DOI: https://doi.org/10.1007/s12044-007-0006-0