Literature cited
F. V. Atkinson, “On second-order differential inequalities,” Proc. R. Soc. Edinburgh,72, 109–127 (1972/73).
Lu-San Chen, “On the nonoscillatory properties of solutions of a functional differential equation,” Bull. Soc. Math. Grèce,17, 11–19 (1976).
M. K. Grammatikopoulos, “Oscillatory and asymptotic behavior of differential equations with deviating arguments,” Hiroshima Math. J.,6, 31–53 (1976).
M. K. Grammatikopoulos, “On the oscillatory character of bounded solutions of differential equations with perturbed arguments,” Chekhoslovatskii Mat. Zh.,27, 186–200 (1977).
M. K. Grammatikopoulos, Y. G. Sficas, and V. A. Staikos, “Oscillatory properties of strongly superlinear differential equations with deviating arguments,” J. Math. Anal. Appl. (to appear).
G. H. Hardy and J. E. Littlewood, “Contributions to the arithmatic theory of series,” Proc. London Math. Soc.,11, 411–478 (1913).
A. G. Kartsatos, “On the maintenance of oscillations of n-th-order equations under the effect of a small forcing term,” J. Different. Equations,10, 355–363 (1971).
A. G. Kartsatos, “On positive solutions of perturbed nonlinear differential equations,” J. Math. Anal. Appl.,47, 58–68 (1974).
I. T. Kiguradze, “On the oscillatory character of solutions of the equation dmu/dtm +a(t)¦u¦nsgnu = 0,” Mat. Sb.,65, 172–187 (1964).
I. T. Kiguradze, “On the question of the oscillatory character of solutions of nonlinear differential equations,” Differents. Uravn.,1, 995–1006 (1965).
R. G. Koplatadze, “On oscillatory solutions of second order delay differential inequalities,” J. Math. Anal. Appl.,42, 148–157 (1973).
R. G. Koplatadze, “A remark on the oscillatory character of solutions of differential inequalities and equations of high order with delayed argument,” Differents. Uravn.,10, 1400–1405 (1974).
T. Kusano, “Oscillatory behavior of higher order retarded differential equations,” in: Proceedings of Carathèodory International Symposium (Athens, September 3–7, 1973), The Greek Math. Soc., pp.370-–389.
T. Kusano and H. Onose, “Nonoscillation theorems for differential equations with deviating arguments,” Pac. J. Math.,63, 185–192 (1976).
T. Kusano and H. Onose, “Asymptotic behavior of nonoscillatory solutions of nonlinear differential equations with forcing term,” Ann. Mat. Pure Appl.,112, 231–240 (1977).
T. Kusano and H. Onose, “Asymptotic behavior of nonoscillatory solutions of functional equations of arbitrary order,” J. London Math. Soc.,14, 106–112 (1976).
B. S. Lalli and R. P. Jahagirdar, “Oscillatory properties of a second order nonlinear functional differential equation,” in: Proceedings of Carathèodory International Symposium (Athens, September 3–7, 1973), The Greek Math. Soc., pp. 390–396.
P. Marušiak, “Oscillation of solutions of nonlinear delay differential equations,” Mat. Časopis Sloven. Akad. Vied.,24, 371–380 (1974).
M. Naito, “Oscillations of differential inequalities with retarded arguments,” Hiroshima Math, J.,5, 187–192 (1975).
J. Schauder, “Der Fixpunktsatz in Funktionalräumen,” Stud. Math.,2, 171–180 (1930).
B. Singh, “Nonoscillation of forced fourth-order retarded equations,” SIAM J. Appl. Math.,28, 265–269 (1975).
B. Singh, “Asymptotic nature of nonoscillatory solutions of n-th-order retarded differential equations,” SIAM J. Math. Anal.,6, 784–795 (1975).
V. A. Staikos and Ch. G. Philos, “On the asymptotic behavior of nonoscillatory solutions of differential equations with deviating arguments,” Hiroshima Math. J.,7, 9–31 (1977).
V. A. Staikos and Ch. G. Philos, “Asymptotic properties of nonoscillatory solutions of differential equations with deviating arguments,” Pac. J. Math.,70, 221–242 (1977).
V. A. Staikos and Y. G. Sficas, “Forced oscillations for differential equations of arbitrary order,” J. Different. Equations,17, 1–11 (1975).
V. A. Staikos and Y. G. Sficas, “Criteria for asymptotic and oscillatory character of functional differential equations of arbitrary order,” Boll. Un. Mat. Ital.,6, 185–192 (1972).
M. Švec, “Fixpunktsatz und monotone Lösungen der Differentialgleichung y(n) + B(x, y, y',..., y(n−1)) · y = 0,” Arch. Math. (Brno),2, 43–55 (1966).
M. Svec, “Monotone solutions of some differential equations,” Colloq. Math.,18, 7–21 (1967).
M. Svec, “Les propriétés asymptotiques des solutions d'une équation différentielle nonlinéaire d'order n,” Czechoslovak Math. J.,17, 550–557 (1967).
H. Teufel, Jr., “A note on second order differential inequalities and functional differential equations,” Pac. J. Math.,41, 537–541 (1972).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol.31, No. 6, pp. 705–716, November–December, 1979.
Rights and permissions
About this article
Cite this article
Staikos, V.A. Asymptotic behavior and oscillatory character of bounded solutions of differential equations with deviating arguments. Ukr Math J 31, 544–553 (1979). https://doi.org/10.1007/BF01092536
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01092536