×

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


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
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Brewer, D.W, A nonlinear semigroup for a functional differential equation, () · Zbl 0793.34049
[2] Browder, F, Nonlinear equations of evolution, Ann. math., 80, 485-523, (1964) · Zbl 0127.33602
[3] {\scJ. Dyson and R. Villella Bressan}, Functional differential equations operators, Edinburgh J. Math., to appear. · Zbl 0361.34055
[4] {\scW. Fitzgibbon}, Nonlinear Volterra equations with infinite delay, Monatsh. Math., to appear. · Zbl 0382.45003
[5] {\scW. Fitzgibbon}, Stability for abstract nonlinear Volterra equations involving finite delay, J. Math. Anal. Appl., to appear. · Zbl 0382.45003
[6] Friedman, A, Partial differential equations, (1969), Holt, Rinehart, and Winston New York
[7] Hale, J, Functional differential equations, () · Zbl 0222.34003
[8] Krein, S.G, Linear differential equations in Banach space, (1971), Amer. Math. Soc Providence, R.I · Zbl 0636.34056
[9] Ladas, G; Lakshmikantham, V, Differential equations in abstract spaces, (1972), 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] {\scC. Travis and G. Webb}, Existence, stability, and compactness in the α-norm for partial functional differential equations, to appear. · 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] {\scG. Webb}, Asymptotic stability for abstract nonlinear functional differential equations, Proc. Amer. Math. Soc., to appear. · Zbl 0324.34079
[17] Yosida, K, Functional analysis, (1968), 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 San Francisco
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.