An oscillation criteria for third order neutral delay differential equations

• Autorzy: Han Z. , Li T. , Sun S. , Zhang C.
• 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.

Słowa kluczowe

EN

oscillation; third order; neutral delay differential equations

PL

oscylacja; neutralne opóźnione równanie różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2010
• Tom: Vol. 16, nr 2
• Strony: 295--303
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Han Z.

autor

Li T.

autor

Sun S.

autor

Zhang C.

• School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, PR. China,

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.