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Oscillation of first-order nonlinear differential equations with deviating arguments. (English) Zbl 0433.34051

MSC:
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
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[1] Clifford H. Anderson, Asymptotic oscillation results for solutions to first-order nonlinear differential-difference equations of advanced type, J. Math. Anal. Appl. 24 (1968), 430 – 439. · Zbl 0191.10703 · doi:10.1016/0022-247X(68)90041-3 · doi.org
[2] R. G. Koplatadze, The oscillating solutions of nonlinear first order differential equations with retarded argument, Sakharth. SSR Mecn. Akad. Moambe 70 (1973), 17 – 20 (Russian, with Georgian and English summaries). · Zbl 0261.34045
[3] G. Ladas, Sharp conditions for oscillations caused by delays, Tech. Rep. Univ. Rhode Island, No. 64, 1976. · Zbl 0407.34055
[4] G. Ladas, V. Lakshmikantham, and J. S. Papadakis, Oscillations of higher-order retarded differential equations generated by the retarded argument, Delay and functional differential equations and their applications (Proc. Conf., Park City, Utah, 1972) Academic Press, New York, 1972, pp. 219 – 231. · Zbl 0273.34052
[5] James C. Lillo, Oscillatory solutions of the equation \?\(^{\prime}\)(\?)=\?(\?)\?(\?-\?(\?)), J. Differential Equations 6 (1969), 1 – 35. · Zbl 0174.39804 · doi:10.1016/0022-0396(69)90114-4 · doi.org
[6] Ch. G. Philos, Oscillations caused by delays, An. Ştiinţ. Univ. ”Al. I. Cuza” Iaşi Secţ. I a Mat. (N.S.) 24 (1978), no. 1, 71 – 76. · Zbl 0398.34064
[7] A. N. Šarkovskii and V. V. Ševelo, On oscillations generated by retardations, Mechanics, Third Congress, Varna, 1977, pp. 49-52. (Russian)
[8] Y. G. Sficas and V. A. Staïkos, The effect of retarded actions on nonlinear oscillations, Proc. Amer. Math. Soc. 46 (1974), 259 – 264. · Zbl 0263.34075
[9] Warren E. Shreve, Oscillation in first order nonlinear retarded argument differential equations, Proc. Amer. Math. Soc. 41 (1973), 565 – 568. · Zbl 0254.34075
[10] Alexander Tomaras, Oscillations of an equation relevant to an industrial problem, Bull. Austral. Math. Soc. 12 (1975), no. 3, 425 – 431. · Zbl 0299.34101 · doi:10.1017/S0004972700024084 · doi.org
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