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## Open Mathematics

2011 | 9 | 1 | 184-195
Tytuł artykułu

### Unbounded solutions of third order delayed differential equations with damping term

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Globally positive solutions for the third order differential equation with the damping term and delay, $$x''' + q(t)x'(t) - r(t)f(x(\phi (t))) = 0,$$ are studied in the case where the corresponding second order differential equation $$y'' + q(t)y = 0$$ is oscillatory. Necessary and sufficient conditions for all nonoscillatory solutions of (*) to be unbounded are given. Furthermore, oscillation criteria ensuring that any solution is either oscillatory or unbounded together with its first and second derivatives are presented. The comparison of results with those in the case when (**) is nonoscillatory is given, as well.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
184-195
Opis fizyczny
Daty
wydano
2011-02-01
online
2010-12-30
Twórcy
autor
• Masaryk University
autor
• University of Florence
autor
• Masaryk University
autor
• University of Florence
Bibliografia
• [1] Bartušek M., On noncontinuable solutions of differential equations with delay, Electron. J. Qual. Theory Differ. Equ., 2009, Spec. Ed. I, No. 6
• [2] Bartušek M., Cecchi M., Došlá Z., Marini M., On nonoscillatory solutions of third order nonlinear differential equations, Dynam. Systems Appl., 2000, 9(4), 483–499
• [3] Bartušek M., Cecchi M., Došlá Z., Marini M., Oscillation for third order nonlinear differential equations with deviating argument, Abstr. Appl. Anal., 2010, Art. ID 278962
• [4] Bartušek M., Cecchi M., Došlá Z., Marini M., Positive solutions of third order damped nonlinear differential equations, Math. Bohem. (in press)
• [5] Borůvka O., Linear Differential Transformations of the Second Order, The English Universities Press, London, 1971
• [6] Cecchi M., Došlá Z., Marini M., Asymptotic behavior of solutions of third order delay differential equations, Arch. Math. (Brno), 1997, 33(1–2), 99–108
• [7] Cecchi M., Došlá Z., Marini M., On nonlinear oscillations for equations associated to disconjugate operators, Nonlinear Anal., 1997, 30(3), 1583–1594 http://dx.doi.org/10.1016/S0362-546X(97)00028-X
• [8] Cecchi M., Došlá Z., Marini M., On third order differential equations with property A and B, J. Math. Anal. Appl., 1999, 231(2), 509–525 http://dx.doi.org/10.1006/jmaa.1998.6247
• [9] Džurina J., Asymptotic properties of the third order delay differential equations, Nonlinear Anal., 1996, 26(1), 33–39 http://dx.doi.org/10.1016/0362-546X(94)00239-E
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• [14] Heidel J.W., Qualitative behavior of solutions of a third order nonlinear differential equations, Pacific J. Math., 1968, 27(3), 507–526
• [15] Kiguradze I.T., An oscillation criterion for a class of ordinary differential equations, Differential Equations, 1992, 28(2), 180–190
• [16] Kiguradze I., Chanturia T.A., Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Math. Appl. (Soviet Ser.), 89, Kluwer, Dordrecht, 1993
• [17] Marini M., Criteri di limitatezza per le soluzioni dell'equazione lineare del secondo ordine, Boll. Un. Mat. Ital., 1975, 11(1), 154–165
• [18] Mojsej I., Ohriska J., Comparison theorems for noncanonical third order nonlinear differential equations, Cent. Eur. J. Math., 2007, 5(1), 154–163 http://dx.doi.org/10.2478/s11533-006-0044-3
• [19] Mojsej I., Tartal'ová A., On bounded nonoscillatory solutions of third-order nonlinear differential equations, Cent. Eur. J. Math., 2009, 7(4), 717–724 http://dx.doi.org/10.2478/s11533-009-0054-z
• [20] Parhi N., Padhi S., On asymptotic behavior of delay-differential equations of third order, Nonlinear Anal., 1998, 34(3), 391–403 http://dx.doi.org/10.1016/S0362-546X(97)00600-7
• [21] Saker S.H., Oscillation criteria of Hille and Nehari types for third order delay differential equations, Commun. Appl. Anal., 2007, 11(3–4), 451–468
• [22] Tiryaki A., Aktaş M.F., Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl., 2007, 325(1), 54–68 http://dx.doi.org/10.1016/j.jmaa.2006.01.001
Typ dokumentu
Bibliografia
Identyfikatory