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2009 | 7 | 4 | 717-724
Tytuł artykułu

On bounded nonoscillatory solutions of third-order nonlinear differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. We give the necessary and sufficient conditions guaranteeing the existence of bounded nonoscillatory solutions. Sufficient conditions are proved via a topological approach based on the Banach fixed point theorem.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
4
Strony
717-724
Opis fizyczny
Daty
wydano
2009-12-01
online
2009-10-31
Twórcy
autor
  • Institute of Mathematics, Faculty of Science, P. J. Šafárik University, Košice, Slovak Republic, ivan.mojsej@upjs.sk
  • Department of Applied Mathematics and Business Informatics, Faculty of Economics, Technical University, Košice, Slovak Republic, alena.tartalova@tuke.sk
Bibliografia
  • [1] Agarwal R.P., Bohner M., Li W.T., Nonoscillation and oscillation: Theory for functional differential equations, Pure Appl. Math. 267, Dekker, New York, 2004
  • [2] Bartušek M., On oscillatory solutions of third order differential equation with quasiderivatives, Electron. J. Differ. Equ. Conf., 1999, 03, 1–11
  • [3] Bartušek M., On the structure of solutions of a system of three differential inequalities, Arch. Math. (Brno), 1994, 30, 117–130
  • [4] Cecchi M., Došlá Z., Marini M., Comparison theorems for third order differential equations, Proceeding of Dynam. Systems Appl., 1996, 2, 99–106
  • [5] 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[Crossref]
  • [6] Cecchi M., Došlá Z., Marini M., An equivalence theorem on properties A, B for third order differential equations, Ann. Mat. Pura Appl. (IV), 1997, CLXXIII, 373–389 http://dx.doi.org/10.1007/BF01783478[Crossref]
  • [7] Cecchi M., Marini M., Villari G., On some classes of continuable solutions of a nonlinear differential equation, J. Differential Equations, 1995, 118, 403–419 http://dx.doi.org/10.1006/jdeq.1995.1079[Crossref]
  • [8] 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[Crossref]
  • [9] Džurina J., Comparison theorems for functional differential equations, EDIS-Žilina University Publisher, Žilina, 2002
  • [10] Kiguradze I., On asymptotic properties of solutions of third order linear differential equations with deviating arguments, Arch. Math. (Brno), 1994, 30, 59–72
  • [11] Knežo D., Šoltés V., Existence and properties of nonoscillatory solutions of third order differential equation, Fasc. Math., 1995, 25, 63–74
  • [12] Ladde G.S., Lakshmikantham V., Zhang B.G., Oscillation theory of differential equations with deviating arguments, Pure Appl. Math., 110, Dekker, New York, 1987
  • [13] Mihalíková B., Džurina J., Oscillations of advanced differential equations, Fasc. Math., 1995, 25, 95–103
  • [14] Mojsej I., Asymptotic properties of solutions of third-order nonlinear differential equations with deviating argument, Nonlinear Anal., 2008, 68(11), 3581–3591 http://dx.doi.org/10.1016/j.na.2007.04.001[Crossref]
  • [15] 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[Crossref][WoS]
  • [16] Parhi N., Padhi S., Asymptotic behaviour of a class of third order delay differential equations, Math. Slovaca, 2000, 50(3), 315–333
  • [17] Philos Ch.G., Sficas Y.G., Oscillatory and asymptotic behavior of second and third order retarded differential equations, Czechoslovak Math. J., 1982, 32(107), 169–182
  • [18] Tiryaki A., Aktaš 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[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0054-z
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