Density of slowly oscillating solutions of x(t)=-f(x(t-1)). (English) Zbl 0451.34063


34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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[1] Chow, S.N; Mallet-Paret, J, Integral averaging and bifurcation, J. differential equations, 26, 112-159, (1977) · Zbl 0367.34033
[2] Hale, J, Theory of functional differential equations, (1977), Springer-Verlag Berlin-Heidelberg-New York
[3] Hale, J; Perello, C, The neighborhood of a singular point for functional differential equations, Contrib. differential equations, 3, 351-375, (1964) · Zbl 0136.07901
[4] Kaplan, J; Yorke, J, On the stability of a periodic solution of a differential delay equation, SIAM J. math. anal., 6, 268-282, (1975) · Zbl 0241.34080
[5] Nussbaum, R.D, Periodic solutions of nonlinear autonomous functional differential equations, (), 283-325
[6] Nussbaum, R.D, Uniqueness and nonuniqueness for periodic solutions of x′(t) = −g(x(t − 1)), J. differential equations, 34, 25-54, (1979) · Zbl 0404.34057
[7] {\scH. Peters}, personal communication, 1978.
[8] Walther, H.O, Über ejektivität und periodische Lösungen bei autonomen funktional-differentialgleichungen mit verteilter verzögerung, (1977), Habilitationsschrift Munich
[9] Walther, H.O, On instability, ω-limit sets and periodic solutions of nonlinear autonomous differential delay equations, () · Zbl 0345.34057
[10] Wright, E.M, A nonlinear difference-differential equation, J. reine angew. math., 194, 66-87, (1955) · Zbl 0064.34203
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