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. 1978 Uniform asymptotic stability in functional differential equations Proc. Amer. Math. Soc. 68 195 – 199 10.1090/S0002

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.1016/S0895-7177(97)00141-6 . [2] Agarwal , R. P. , Grace , S. R. , O’Regan , D. 2003 On the oscillation of certain functional differential equations via comparison methods J. Math. Anal

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functional differential equation, Math. Nachr. 217 (2000), 175–186. MR 2001f :35243 Simon L. On nonlinear hyperbolic functional differential equation

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In the present paper, by means of the successive approximations method, the local or global existence and uniqueness theorems for a stochastic functional differential equation of the Ito type are proved.

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Pelczar, A., Some functional differential equations, Dissert. Math. 100 (1973), 3-110. MR 49 #11074 Some functional differential equations Dissert. Math

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Abstract  

We establish the existence of mild solutions and periodic mild solutions for a class of abstract first-order non-autonomous neutral functional differential equations with infinite delay in a Banach space.

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The existence of an algebraic functional-differential equation P (y′(x), y′(x + log 2), …, y′(x + 5 log 2)) = 0 is proved such that the real-analytic solutions are dense in the space of continuous functions on every compact interval. A similar result holds for an algebraic functional-differential equation P(y′(x − 4πi), y′(x − 2πi), …, y′(x + 4πi)) = 0 (with i 2 = −1), which is explicitly given: There are real-analytic solutions on the real line such that every continuous function defined on a compact interval can be approximated by these solutions with arbitrary accuracy.

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Abstract  

We consider half-linear retarded functional differential equations of the form

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(|x'(t)|^\alpha \operatorname{sgn} x'(t))' = q(t)|x(g(t))|^\alpha \operatorname{sgn} x(g(t)), \alpha > 0, g(t) < t$$ \end{document}
and obtain a necessary and sufficient condition to possess a slowly varying solution and a regularly varying solution of index 1 at the same time.

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