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Asymptotic behavior and oscillatory character of bounded solutions of differential equations with deviating arguments

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Literature cited

  1. F. V. Atkinson, “On second-order differential inequalities,” Proc. R. Soc. Edinburgh,72, 109–127 (1972/73).

    Google Scholar 

  2. Lu-San Chen, “On the nonoscillatory properties of solutions of a functional differential equation,” Bull. Soc. Math. Grèce,17, 11–19 (1976).

    Google Scholar 

  3. M. K. Grammatikopoulos, “Oscillatory and asymptotic behavior of differential equations with deviating arguments,” Hiroshima Math. J.,6, 31–53 (1976).

    Google Scholar 

  4. M. K. Grammatikopoulos, “On the oscillatory character of bounded solutions of differential equations with perturbed arguments,” Chekhoslovatskii Mat. Zh.,27, 186–200 (1977).

    Google Scholar 

  5. 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).

  6. G. H. Hardy and J. E. Littlewood, “Contributions to the arithmatic theory of series,” Proc. London Math. Soc.,11, 411–478 (1913).

    Google Scholar 

  7. 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).

    Google Scholar 

  8. A. G. Kartsatos, “On positive solutions of perturbed nonlinear differential equations,” J. Math. Anal. Appl.,47, 58–68 (1974).

    Google Scholar 

  9. 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).

    Google Scholar 

  10. I. T. Kiguradze, “On the question of the oscillatory character of solutions of nonlinear differential equations,” Differents. Uravn.,1, 995–1006 (1965).

    Google Scholar 

  11. R. G. Koplatadze, “On oscillatory solutions of second order delay differential inequalities,” J. Math. Anal. Appl.,42, 148–157 (1973).

    Google Scholar 

  12. 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).

    Google Scholar 

  13. 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.

  14. T. Kusano and H. Onose, “Nonoscillation theorems for differential equations with deviating arguments,” Pac. J. Math.,63, 185–192 (1976).

    Google Scholar 

  15. 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).

    Google Scholar 

  16. T. Kusano and H. Onose, “Asymptotic behavior of nonoscillatory solutions of functional equations of arbitrary order,” J. London Math. Soc.,14, 106–112 (1976).

    Google Scholar 

  17. 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.

  18. P. Marušiak, “Oscillation of solutions of nonlinear delay differential equations,” Mat. Časopis Sloven. Akad. Vied.,24, 371–380 (1974).

    Google Scholar 

  19. M. Naito, “Oscillations of differential inequalities with retarded arguments,” Hiroshima Math, J.,5, 187–192 (1975).

    Google Scholar 

  20. J. Schauder, “Der Fixpunktsatz in Funktionalräumen,” Stud. Math.,2, 171–180 (1930).

    Google Scholar 

  21. B. Singh, “Nonoscillation of forced fourth-order retarded equations,” SIAM J. Appl. Math.,28, 265–269 (1975).

    Google Scholar 

  22. B. Singh, “Asymptotic nature of nonoscillatory solutions of n-th-order retarded differential equations,” SIAM J. Math. Anal.,6, 784–795 (1975).

    Google Scholar 

  23. 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).

    Google Scholar 

  24. 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).

    Google Scholar 

  25. V. A. Staikos and Y. G. Sficas, “Forced oscillations for differential equations of arbitrary order,” J. Different. Equations,17, 1–11 (1975).

    Google Scholar 

  26. 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).

    Google Scholar 

  27. 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).

    Google Scholar 

  28. M. Svec, “Monotone solutions of some differential equations,” Colloq. Math.,18, 7–21 (1967).

    Google Scholar 

  29. M. Svec, “Les propriétés asymptotiques des solutions d'une équation différentielle nonlinéaire d'order n,” Czechoslovak Math. J.,17, 550–557 (1967).

    Google Scholar 

  30. H. Teufel, Jr., “A note on second order differential inequalities and functional differential equations,” Pac. J. Math.,41, 537–541 (1972).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.31, No. 6, pp. 705–716, November–December, 1979.

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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

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