PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2010 | 8 | 6 | 1091-1103
Tytuł artykułu

On the asymptotic behavior of a class of third order nonlinear neutral differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The objective of this paper is to study asymptotic properties of the third-order neutral differential equation $$ \left[ {a\left( t \right)\left( {\left[ {x\left( t \right) + p\left( t \right)x\left( {\sigma \left( t \right)} \right)} \right]^{\prime \prime } } \right)^\gamma } \right]^\prime + q\left( t \right)f\left( {x\left[ {\tau \left( t \right)} \right]} \right) = 0, t \geqslant t_0 . \left( E \right) $$. We will establish two kinds of sufficient conditions which ensure that either all nonoscillatory solutions of (E) converge to zero or all solutions of (E) are oscillatory. Some examples are considered to illustrate the main results.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
6
Strony
1091-1103
Opis fizyczny
Daty
wydano
2010-12-01
online
2010-10-30
Twórcy
Bibliografia
  • [1] Akın-Bohner E., Došlá Z., Lawrence B., Oscillatory properties for three-dimensional dynamic systems, Nonlinear Anal., 2008, 69(2), 483–494 http://dx.doi.org/10.1016/j.na.2007.05.035
  • [2] Baculíková B., Džurina J., Oscillation of third-order neutral differential equations, Math. Comput. Modelling, 2010, 52(1–2), 215–226 http://dx.doi.org/10.1016/j.mcm.2010.02.011
  • [3] Baculíková B., Elabbasy E.M., Saker S.H., Džurina J., Oscillation criteria for third-order nonlinear differential equations, Math. Slovaca, 2008, 58(2), 201–220 http://dx.doi.org/10.2478/s12175-008-0068-1
  • [4] Baĭnov D.D., Mishev D.P., Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, Bristol, 1991
  • [5] Džurina J., Asymptotic properties of third order delay differential equations, Czechoslovak Math. J., 1995, 45(120)(3), 443–448
  • [6] 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
  • [7] Džurina J., Oscillation theorems for neutral differential equations of higher order, Czechoslovak Math. J., 2004, 54(129)(1), 107–117 http://dx.doi.org/10.1023/B:CMAJ.0000027252.29549.bb
  • [8] Džurina J., Baculíková B., Oscillation of third-order functional differential equations, Electron. J. Qual. Theory Differ. Equ., 2010, No. 43
  • [9] Erbe L.H., Kong Q., Zhang B.G., Oscillation Theory for Functional-Differential Equations, Monogr. Textbooks Pure Appl. Math., 190, Marcel Dekker, New York, 1995
  • [10] Grace S.R., Agarwal R.P., Pavani R., Thandapani E., On the oscillation of certain third order nonlinear functional differential equations, Appl. Math. Comput., 2008, 202(1), 102–112 http://dx.doi.org/10.1016/j.amc.2008.01.025
  • [11] Greguš M., Third Order Linear Differential Equations, Math. Appl. (East European Ser.), Reidel, Dordrecht, 1987
  • [12] Györi I., Ladas G., Oscillation Theory of Delay Differential Equations, Oxford Math. Monogr., Clarendon Press, Oxford, 1991
  • [13] Hassan T.S., Oscillation of third order nonlinear delay dynamic equations on time scales, Math. Comput. Modelling, 2009, 49(7–8), 1573–1586 http://dx.doi.org/10.1016/j.mcm.2008.12.011
  • [14] Kiguradze I.T., Chanturia T.A., Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Math. Appl. (Soviet Ser.), 89, Kluwer Acad. Publ., Dordrecht, 1993
  • [15] Kusano T., Naito M., Comparison theorems for functional-differential equations with deviating arguments, J. Math. Soc. Japan, 1981, 33(3), 509–533 http://dx.doi.org/10.2969/jmsj/03330509
  • [16] Lacková D., The asymptotic properties of the solutions of the nth order functional neutral differential equations, Appl. Math. Comput., 2003, 146(2–3), 385–392 http://dx.doi.org/10.1016/S0096-3003(02)00590-8
  • [17] Ladde G.S., Lakshmikantham V., Zhang B.G., Oscillation Theory of Differential Equations with Deviating Arguments, Monogr. Textbooks Pure Appl. Math., 110, Marcel Dekker, New York, 1987
  • [18] Lazer A.C., The behavior of solutions of the differential equation y’" + p(x)y’ + q(x)y = 0, Pacific J. Math., 1966, 17(3), 435–466
  • [19] Parhi N., Das P., Asymptotic property of solutions of a class of third-order differential equations, Proc. Amer. Math. Soc., 1990, 110(2), 387–393
  • [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] Parhi N., Padhi S., Asymptotic behaviour of solutions of third order delay-differential equations, Indian J. Pure Appl. Math., 2002, 33(10), 1609–1620
  • [22] Philos Ch.G., On the existence of nonoscillatory solutions tending to zero at 1 for differential equations with positive delays, Arch. Math. (Basel), 1981, 36(2), 168–178
  • [23] Saker S.H., Oscillation criteria of third-order nonlinear delay differential equations, Math. Slovaca, 2006, 56(4), 433–450
  • [24] Saker S.H., Džurina J., On the oscillation of certain class of third-order nonlinear delay differential equations, Math. Bohemica, 2010, 135(3), 225–237
  • [25] Tanaka K., Asymptotic analysis of odd order ordinary differential equations, Hiroshima Math. J., 1980, 10(2), 391–408
  • [26] Tiryaki A., Aktas 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
  • [27] Zhong J., Ouyang Z., Zou S., Oscillation criteria for a class of third-order nonlinear neutral differential equations, J. Appl. Anal. (in press)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0072-x
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.