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Asymptotic behavior of solutions of the functional differential equation $$x'(t) =Ax(\lambda t)+Bx(t)$$, $$\lambda >0$$. (English) Zbl 0336.34060

MSC:
 34K05 General theory of functional-differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations
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References:
 [1] Anderson, Clifford H, Asymptotic oscillation results for solutions to first-order nonlinear differential-difference equations of advanced type, J. math. anal. appl., 24, 430-439, (1968) · Zbl 0191.10703 [2] Banks, H.T, The representation of solutions of linear functional differential equations, J. differential eqs., 5, 399-410, (1969) · Zbl 0165.42701 [3] Bellman, R.E; Cooke, K.L, Differential-difference equations, (1963), Academic Press New York [4] De Bruijn, N.G, The difference-differential equations F′(x) = eαx + βF(x − 1), I, II, (), 449-464 · Zbl 0053.38703 [5] De Bruijn, N.G, The asymptotically periodic behavior of the solutions of some linear functional equations, Amer. J. math., 71, 313-330, (1949) · Zbl 0033.27002 [6] Doss, S; Nasr, S.K, On the functional equation $$dydx = f(x, y(x), y(x + h)), h>0$$, Amer. J. math., 75, 713-716, (1953) · Zbl 0053.06101 [7] Dyson, J, The functional-differential equation y′(x) = ay(λx) + by (x) and generalizations, Lecture notes math., 280, 308-313, (1972) [8] Fox, L; Mayers, D.F; Ockendon, J.R; Taylor, A.B, On a functional differential equation, J. inst. math. applics., 8, 271-307, (1971) · Zbl 0251.34045 [9] Frederickson, P.O, Global solutions to certain nonlinear functional-differential equations, J. math. anal. appl., 33, 355-358, (1971) · Zbl 0191.15302 [10] Hale, J.K, Functional differential equations, (1971), Springer-Verlag New York · Zbl 0213.36901 [11] Heard, M.L, Asymptotic behavior of solutions of the functional differential equation x′(t) = ax(t) + bx(tα), α>1, J. math. anal. appl., 44, 745-757, (1973) · Zbl 0289.34115 [12] Heard, M.L, A family of solutions of the initial value problem for the equation x′(t) = ax(λt), λ>1, Aequations mathematicae, 9, 273-280, (1973) · Zbl 0268.34015 [13] Kato, T; McLeod, J.B, The functional-differential equation y′(x) = ay(λx) + by (x), Bull. amer. math. soc., 77, 891-937, (1971) · Zbl 0236.34064 [14] Kato, T, Asymptotic behavior of solutions of the functional differential equation y′(x) = ay(λx) + by(x), (), 197-217 [15] Mahler, K, On a special functional equation, J. London math. soc., 15, 115-123, (1940) · JFM 66.1214.04 [16] McLeod, J.B, The functional-differential equation y′(x) = ay(λx) + by (x) and generalizations, Lecture notes math., 280, 308-313, (1972) · Zbl 0256.34079 [17] Ockendon, J.R; Taylor, A.B, The dynamics of a current collection system for an electric locomotive, (), 447-468 [18] Sugiyama, S, On some problems of functional differential equations with advanced argument, (), 367-382
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