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A change of variables for functional differential equations. (English) Zbl 0318.34069


MSC:

34K05 General theory of functional-differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34K25 Asymptotic theory of functional-differential equations
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[1] Anderson, C. 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] Bellman, R.; Cooke, K., Differential-Difference Equations (1963), Academic Press: Academic Press New York · Zbl 0105.06402
[3] Doss, S.; Nasr, S. K., On the functional equation \(dydx = ƒ(x, y(x), y(x + h)), h > 0\), Amer. J. Math., 75, 713-716 (1953) · Zbl 0053.06101
[4] Driver, R., Existence and continuous dependence of solutions of a neutral functional-differential equation, Arch. Rational Mech. Anal., 19, 149-166 (1965) · Zbl 0148.05703
[5] Hale, J., Functional Differential Equations (1971), Springer-Verlag · Zbl 0222.34003
[6] Hale, J.; Cruz, M. A., Existence, uniqueness and continuous dependence of a neutral functional differential equation, Ann. Mat. Pura Appl., 85, 63-82 (1970) · Zbl 0194.41002
[7] Heard, M. L., Asymptotic behavior of solutions of the functional difference equation \(x\)′\((t) = ax (t) + bx (t^α), α > 1\), J. Math. Anal. Appl., 44, 745-757 (1973) · Zbl 0289.34115
[8] Kato, T.; McLeod, J., The functional-differential equation \(y\)′\((x) = ay (λ) + by (x)\), Bull. Amer. Math. Soc., 77, 891-937 (1971) · Zbl 0236.34064
[9] Kuczma, M., Functional Equations in a Single Variable (1968), Polish Scientific Publishers: Polish Scientific Publishers Warsaw · Zbl 0196.16403
[10] Schröder, E., Über iterierte Funktionen, Math. Ann., 3, 296-322 (1871)
[11] Sugiyama, S., On Some Problems of Functional Differential Equations with Advanced Argument, (Benjamin, W. A., U.S.-Japan Seminar on Differential and Functional Equations. U.S.-Japan Seminar on Differential and Functional Equations, New York (1967)), 367-382 · Zbl 0174.46003
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