The effect of retarded actions on nonlinear oscillations

Sficas, Y. G.; Staïkos, V. A.

doi:10.1090/S0002-9939-1974-0355268-1

The effect of retarded actions on nonlinear oscillations
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by Y. G. Sficas and V. A. Staïkos PDF

Proc. Amer. Math. Soc. 46 (1974), 259-264 Request permission

Abstract:

We study the oscillatory and asymptotic behavior of nonlinear retarded differential equations of the form ${x^{(n)}}(t) + {( - 1)^{n + 1}}p(t) \cdot \phi (x[g(t)]) = 0$ under certain conditions which do not hold in the particular case $g(t) \equiv t$ of ordinary differential equations.

References

Takaŝi Kusano and Hiroshi Onose, Oscillation of solutions of nonlinear differential delay equations of arbitrary order, Hiroshima Math. J. 2 (1972), 1–13. MR 324175
G. Ladas, Oscillation and asymptotic behavior of solutions of differential equations with retarded argument, J. Differential Equations 10 (1971), 281–290. MR 291590, DOI 10.1016/0022-0396(71)90052-0
G. Ladas and V. Lakshmikantham, Oscillations caused by retarded actions, Applicable Anal. 4 (1974/75), 9–15. MR 430470, DOI 10.1080/00036817408839080
G. Ladas, G. Ladde, and J. S. Papadakis, Oscillations of functional-differential equations generated by delays, J. Differential Equations 12 (1972), 385–395. MR 333399, DOI 10.1016/0022-0396(72)90039-3
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. MR 0387776
Pavol Marušiak, Note on the Ladas’ paper on “Oscillation and asymptotic behavior of solutions of differential equations with retarded argument” (J. Differential Equations 10 (1971), 281–290) by G. Ladas, J. Differential Equations 13 (1973), 150–156. MR 355266, DOI 10.1016/0022-0396(73)90037-5
Nicolas Minorsky, Nonlinear oscillations, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1962. MR 0137891
Hiroshi Onose, Some oscillation criteria for $n$th order nonlinear delay-differential equations, Hiroshima Math. J. 1 (1971), 171–176. MR 312032
Y. G. Sficas, On oscillation and asymptotic behavior of a certain class of differential equations with retarded argument, Utilitas Math. 3 (1973), 239–249. MR 322316
Y. G. Sficas and V. A. Staïkos, Oscillations of retarded differential equations, Proc. Cambridge Philos. Soc. 75 (1974), 95–101. MR 333402, DOI 10.1017/s0305004100048283
V. A. Staïkos and Y. G. Sficas, Oscillatory and asymptotic behavior of functional differential equations, J. Differential Equations 12 (1972), 426–437. MR 330707, DOI 10.1016/0022-0396(72)90016-2
V. A. Staïkos and Y. G. Sficas, Oscillatory and asymptotic properties of differential equations with retarded arguments, Applicable Anal. 5 (1975), no. 2, 141–148. MR 404811, DOI 10.1080/00036817508839116