Literature cited
C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York-London (1968), p. 220.
K. Kreith, Oscillation Theory, Springer-Verlag, Berlin-Heidelberg-New York (1973), p. 109.
I. T. Kiguradze, Some Singular Boundary-Value Problems for Ordinary Differential Equations [in Russian], Izd Tbilissk. Univ. (1975), p. 352.
V. N. Shevelo, “Problems, methods, and basic results in theory of oscillation of the solutions of nonlinear nonautonomous differential equations,” in: Proceedings of the Second All-Union Session on Theoretical and Applied Mechanics [in Russian], No. 2, Nauka, Moscow (1965), pp. 142–157.
J. Wong, “On second-order nonlinear oscillation,” Funkcialaj Ekvacioj,11, No. 3, 207–234 (1968).
W. B. Fite, “Properties of the solutions of certain functional differential equations,” Trans. Am. Math. Soc.,22, No. 3, 311–319 (1921).
A. D. Myshkis, Linear Differential Equations with Delayed Argument [in Russian], Nauka, Moscow (1972), p. 351.
S. B. Norkin, Differential Equations of the Second Order with Retarded Argument, American Mathematical Society, Providence, R. I. (1972).
S. B. Norkin, “Oscillation of the solutions of differential equations with deviating argument,” in: Differential Equations with Deviating Argument [in Russian], Naukova Dumka, Kiev (1977), pp. 226–236.
Ya. B. Pesin, “On the behavior of the solutions of a strongly nonlinear differential equation with retarded argument,” Differents. Uravn.,10, No. 6, 25–36 (1974).
A. Tomaras, “Oscillations of an equation relevant to an industrial problem,” Bull. Austral. Math. Soc.,12, No. 3, 425–431 (1975).
W. E. Shreve, “Oscillation in first order nonlinear retarded argument differential equations,” Proc. Am. Math. Soc.,41, No. 2, 365–368 (1973).
R. G. Koplatadze, “On the oscillating solutions of nonlinear first-order differential equations with retarded argument,” Soobshch. Akad Nauk Gruz. SSR,70, No. 1, 18–20 (1973).
V. N. Shevelo and O. N. Odarich, “Some topics in theory of oscillation (nonoscillation) of the solutions of second-order differential equations with retarded argument,” Ukr. Mat. Zh.,23, No. 4, 508–516 (1971).
V. N. Shevelo and N. V. Varekh, “On the oscillatory properties of the solutions of linear higher order differential equations with retarded argument,” Ukr. Mat. Zh.,24, No. 4, 513–520 (1972).
V. N. Shevelo and N. V. Varekh, “On some properties of the solutions of retarded differential equations,” Ukr. Mat. Zh.,24, No. 6, 807–813 (1972).
V. N. Shevelo and N. V. Varekh, “On some oscillation theorems for higher order differential equations,” Mathematical Physics [in Russian], No. 13, Naukova Dumka, Kiev (1973), pp. 183–189.
T. Kusano and H. Onose, “Oscillation theorems for delay equations of arbitrary order,” Hiroshima Math. J.,2, No. 2, 263–270 (1972).
Y. G. Sficas and V. Staikos, “Oscillations of retarded differential equations,” Proc. Cambridge Philos. Soc.,55, No. 1, 95–101 (1974).
Y. G. Sficas, “The effect of the delay on the oscillatory and asymptotic behavior of n-th order retarded differential equations,” J. Math. Anal. Appl.,49, No. 3, 748–757 (1975).
J. Werbowski, “On oscillation criteria for differential equations with retarded argument,” Fasc. Math., No. 7, 11–19 (1973).
V. N. Shevelo and N. V. Varekh, “On the oscillatory properties of the solutions of the equations [r(t) Y(n−1)(t)]' +p(t)f(y(τ(t))) = 0,” Ukr. Mat. Zh.,25, No. 5, 724–737 (1973).
O. N. Odarich and V. N. Shevelo, “Some problems of the asymptotic behavior of the solutions of nonlinear differential equations with retarded argument,” Differents. Uravn.,9, No. 4, 637–646 (1973).
H. Onose, “Oscillation and asymptotic behavior of solutions of retarded differential equations of arbitrary order,” Hiroshima Math. J.,3, No. 2, 333–360 (1973).
M. K. Grammatikopoulos, “Oscillatory and asymptotic behavior of differential equations with deviating arguments,” Hiroshima Math. J.,6, No. 1, 31–53 (1976).
N. V. Azbelev, “On the zeros of solutions of a linear second-order differential equation with retarded argument,” Differents. Uravn.,7, No. 7, 1147–1157 (1971).
G. S. Kung, “Oscillation and nonoscillation of differential equations with a time lag,” SIAM J. Appl. Math.,21, No. 2, 207–213 (1971).
V. A. Deift, “Conditions for nonoscillation for a linear homogeneous differential equation with retarded argument,” Differents. Uravn.,10, No. 11, 1057–1063 (1974).
G. Ladas, G. Ladde, and J. S. Papa dakis, “Oscillations of functional-differential equations generated by delays,” J. Differential Equations,12, No. 2, 385–395 (1972).
L. É. El'sgol'ts and S. B. Norkin, Introduction to Theory of Differential Equations with Deviating A rgument, Holden-Day, San Fransisco (1966).
G. S. Ladde, “Oscillations of nonlinear functional differential equations generated by retarded actions, I, ” Rend. Circ. Mat. Palermo,22, Nos. 1–2, 67–76 (1973).
R. G. Koplatadze, “On the existence of oscillatory solutions of nonlinear differential equations of second order with retarded argument,” Dokl. Akad Nauk SSSR,210, No. 2, 260–262 (1973).
R. G. Koplatadze, “Note on the oscillatory properties of the solutions of differential inequalities and higher-order equations with retarded argument,” Differents. Uravn.,10, No. 8, 1400–1405 (1974).
T. Kusano and H. Onose, “Oscillations of functional differential equations with retarded argument,” J. Differential Equations,15, No. 2, 269–277 (1974).
G. B. Gustafson, “Bounded oscillations of linear and nonlinear delay-differential equations of even order,” J. Math. Anal. Appl.,46, No. 1, 175–189 (1974).
Y. G. Sficas and V. A. Staikos, “The effect of retarded actions on nonlinear oscillations,” Proc. Am. Math. Soc.,46, No. 2, 259–264 (1974).
M. Naito, “Oscillations of differential inequalities with retarded arguments,” Hiroshima Math. J.,5, No. 2, 187–192 (1975).
B. Singh, “Impact of delays on oscillation in general functional equations,” Hiroshima Math. J.,5, No. 3, 351–361 (1975).
R. S. Dahiya, “Nonoscillation generating delay terms in even-order differential equations,” Hiroshima Math. J.,5, No. 3, 385–394 (1975).
B. Singh, “Asymptotically vanishing oscillatory trajectories in second order retarded equations,” SIAM J. Math. Anal.,7, No. 1, 37–44 (1976).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 29, No. 3, pp. 313–323, May–June, 1977.
Rights and permissions
About this article
Cite this article
Mitropol'skii, Y.A., Shevelo, V.N. Development of oscillation theory of the solutions of differential equations with retarded argument. Ukr Math J 29, 235–244 (1977). https://doi.org/10.1007/BF01104469
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01104469