The effect of retarded actions on nonlinear oscillations
Authors:
Y. G. Sficas and V. A. Staïkos
Journal:
Proc. Amer. Math. Soc. 46 (1974), 259-264
MSC:
Primary 34K15
DOI:
https://doi.org/10.1090/S0002-9939-1974-0355268-1
MathSciNet review:
0355268
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Abstract | References | Similar Articles | Additional Information
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.
- 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 https://doi.org/10.1016/0022-0396%2871%2990052-0
- G. Ladas and V. Lakshmikantham, Oscillations caused by retarded actions, Applicable Anal. 4 (1974/75), 9–15. MR 430470, DOI https://doi.org/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 https://doi.org/10.1016/0022-0396%2872%2990039-3
- 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 https://doi.org/10.1016/0022-0396%2873%2990037-5
- 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 https://doi.org/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 https://doi.org/10.1016/0022-0396%2872%2990016-2
- 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 https://doi.org/10.1080/00036817508839116
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Additional Information
Keywords:
Oscillatory solution,
nonoscillatory solution,
oscillations generated by retarded actions
Article copyright:
© Copyright 1974
American Mathematical Society