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2010 | Vol. 16, nr 2 | 295-303
Tytuł artykułu

An oscillation criteria for third order neutral delay differential equations

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we will establish some oscillation criteria for the third-order neutral delay differential equations (x(t) - a(t)x(τ (t)))''' + p(t)x(δ (t)) = 0, t ≥ t 0. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations. Our results in this paper extend the results given in [Hanan, Oscillation criteria for third order differential equations, Pacific J. Math. 11 (1961) 919-944]. Some examples are considered to illustrate the main results.
Wydawca

Rocznik
Strony
295-303
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
autor
autor
autor
  • School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, PR. China, hanzhenlai@163.com
Bibliografia
  • [1] R. P. Agarwal, S. R. Grace, D. O'Regan, Oscillation theory for difference and functional differential equations, Kluwer Acad. Publ., Dordrecht, 2000.
  • [2] L. Erbe, Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equations. Pacific J. Math. 64 (1976) 369-385.
  • [3] J. K. Hale, Theory of functional differential equations. Springer-Verlag, New York, 1977.
  • [4] M. Hanan, Oscillation criteria for third order differential equations. Pacific J. Math. 11 (1961) 919-944.
  • [5] I. T. Kiguradze, T. A. Chaturia, Asymptotic properties of solutions of nonatunomous ordinary differential equations, Kluwer Acad. Publ., Drodrecht 1993.
  • [6] A. C. Lazer, The behavior of solutions of the differential equation x'''(t) + p(t)x'(t) + q(t)x(t) = 0, Pacific J. Math. 17 (1966) 435-466.
  • [7] B. Mehri, On the conditions for the oscillation of solutions of nonlinear third order differential equations, Cas. Pest Math. 101 (1976) 124-124.
  • [8] N. Parhi, P. Das, Asymptotic property of solutions of a class of third-order differential equations, Proc. Amer. Math. Soc. 110 (1990) 387-393
  • [9] N. Parhi, P. Das, Oscillation criteria for a class of nonlinear differential equations of third order, Ann. Polon. Math. 57 (1992) 219-229.
  • [10] N. Parhi, P. Das, Oscillation and nonoscillation of nonhomogeneous third order differential equations, Czechoslovak Math. J. 44 (1994) 443-459.
  • [11] N. Parhi, P. Das, On the oscillation of a class of linear homogeneous third order differential equations. Arch. Math. 34 (1998) 435-443.
  • [12] N. Parhi, P. Das, Asymptotic behavior of a class of third order delay differential equations, Math. Slovaca 50 (2000) 315-333.
  • [13] N. Parhi, S. Padhi, Asymptotic behavior of solutions of third order delay differential equations, Indian J. Pure Appl. Math. 33 (2002) 1609-1620.
  • [14] S. H. Saker, Oscillation criteria of certain class of third-order nonlinear delay differential equations, Math. Slovaca 56 (2006) 433^50.
  • [15] A. Skerlik, An integral condition of oscillation for equation y''' + p(t)y'+q(t)y = 0 with nonnegative coefficients, Arch. Math. 31 (1995) 155-161.
  • [16] A. Tiryaki, S. Yaman, Asymptotic behaviour of a class of nonlinear functional differential equations of third order, Appl. Math. Lett. 14 (2001) 327-332.
  • [17] V. Tryhuk, An oscillation criteria for third order linear differential equations. Arch. Math. 2(1975)99-104.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0033-0009
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