Document Zbl 0392.34041

Semilinear functional differential equations in Banach space. (English) Zbl 0392.34041

J. Differ. Equations 29, 1-14 (1978).

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MSC:

34G20	Nonlinear differential equations in abstract spaces
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34E05	Asymptotic expansions of solutions to ordinary differential equations
34K05	General theory of functional-differential equations

Keywords:

Nonlinear Delayterm; Asymptotic Behavior of Mild Solutions; Volterra Integral Equation; Banach Space; Semilinear Abstract Functional Differential Equations

Citations:

Zbl 0305.47022; Zbl 0345.35013

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Full Text: DOI

References:

[1]	Brewer, D. W., A Nonlinear Semigroup for a Functional Differential Equation, (Dissertation (1975), University of Wisconsin) · Zbl 0793.34049
[2]	Browder, F., Nonlinear equations of evolution, Ann. Math., 80, 485-523 (1964) · Zbl 0127.33602
[3]	J. Dyson and R. Villella BressanEdinburgh J. Math.; J. Dyson and R. Villella BressanEdinburgh J. Math. · Zbl 0361.34055
[4]	W. FitzgibbonMonatsh. Math.; W. FitzgibbonMonatsh. Math. · Zbl 0382.45003
[5]	W. FitzgibbonJ. Math. Anal. Appl.; W. FitzgibbonJ. Math. Anal. Appl. · Zbl 0382.45003
[6]	Friedman, A., Partial Differential Equations (1969), Holt, Rinehart, and Winston: Holt, Rinehart, and Winston New York · Zbl 0224.35002
[7]	Hale, J., Functional Differential Equations, (Appl. Math. Series, Vol. 3 (1971), Springer-Verlag: Springer-Verlag New York) · Zbl 0222.34003
[8]	Krein, S. G., Linear Differential Equations in Banach Space (1971), Amer. Math. Soc: Amer. Math. Soc Providence, R.I · Zbl 0636.34056
[9]	Ladas, G.; Lakshmikantham, V., Differential Equations in Abstract Spaces (1972), Academic Press: Academic Press New York · Zbl 0273.34040
[10]	Pazy, A., A class of semi-linear equations of evolution, Israel J. Math., 20, 23-35 (1975) · Zbl 0305.47022
[11]	Pazy, A., On the differentiability and compactness of semigroups of linear operators, J. Math. Mech., 17, 1131-1139 (1968) · Zbl 0162.45903
[12]	C. Travis and G. Webb; C. Travis and G. Webb · Zbl 0414.34080
[13]	Travis, C.; Webb, G., Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc., 200, 395-418 (1974) · Zbl 0299.35085
[14]	Travis, C.; Webb, G., Partial differential equations with deviating arguments in the time variable, J. Math. Anal. Appl., 56, 397-409 (1976) · Zbl 0349.35071
[15]	Webb, G., Autonomous nonlinear functional differential equations, J. Math. Anal. Appl., 46, 1-12 (1974) · Zbl 0277.34070
[16]	G. WebbProc. Amer. Math. Soc.; G. WebbProc. Amer. Math. Soc. · Zbl 0324.34079
[17]	Yosida, K., Functional Analysis (1968), Springer-Verlag: Springer-Verlag New York · Zbl 0152.32102
[18]	Èl’Sgol’c, L., Introduction to the Theory of Differential Equations with Deviating Arguments (1966), Holden-Day: Holden-Day San Francisco · Zbl 0133.33502

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