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On the delay-differential equations x’(t) + a(t)f(x(t - r(t))) = 0 and x”(t) + a(t)f(x(t - r(t)))=0. (English) Zbl 0344.34065


MSC:

34K20 Stability theory of functional-differential equations
34D20 Stability of solutions to ordinary differential equations
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References:

[1] Haddock, J. R., On the asymptotic behavior of solutions of \(x\)′\((t)\) = −\(a(t) f(x (t\) − \(r(t)))\), SIAM J. Math. Anal., 5, 569-573 (1974) · Zbl 0254.34039
[2] Yorke, J. A., Asymptotic stability for one-dimensional differential-delay equations, J. Differential Equations, 7, 189-202 (1970) · Zbl 0184.12401
[3] Burton, T.; Grimmer, R., On the asymptotic behavior of solutions of \(x\)″ + \(a(t)f(x) = 0\), (Proc. Cambridge Philos. Soc., 70 (1971)), 77-88 · Zbl 0235.34075
[4] Burton, T.; Grimmer, R., Stability properties of \((r(t(u\)′)))′+ \(a(t)f(u)g(u\)′) = 0, Monatsch. Math., 74, 211-222 (1970) · Zbl 0195.09804
[5] Burton, T.; Grimmer, R., On the asymptotic behavior of solutions of \(x\)″ + \(a(t)f(x) = e (t)\), Pacific J. Math., 41, 43-55 (1972) · Zbl 0245.34024
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[9] Driver, R. D., Existence theory for a delay differential system, Contrib. Differential Equations, 1, 317-336 (1963)
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[13] Winston, E., Comparison theorems for scalar delay differential equations, J. Math. Anal. Appl., 29, 455-463 (1970) · Zbl 0188.15703
[14] Winston, E., Uniqueness of the zero solution for delay differential equations with state dependence, J. Differential Equations, 7, 395-405 (1970) · Zbl 0188.15603
[15] Cooke, K. L., Functional differential equations close to differential equations, Bull. Amer. Math. Soc., 72, 285-288 (1966) · Zbl 0151.10401
[16] Halanay, A.; Yorke, J., Some new results and problems in the theory of differential-delay equations, SIAM Rev., 13, 55-80 (1971) · Zbl 0216.11902
[17] Hale, J. K., Functional Differential Equations (1971), Springer-Verlag: Springer-Verlag New York · Zbl 0213.36901
[18] Yoshizawa, T., Stability Theory by Liapunov’s Second Method, Math. Soc. Japan, Tokyo (1966) · Zbl 0144.10802
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