Oscillation criteria for a class of third-order nonlinear neutral differential equations

• Autorzy: Zhong J. , Ouyang Z. , Zou S.
• Języki publikacji: EN

Abstrakty

EN

A class of third-order nonlinear neutral differential equation (r(t)(y"(t)) α)' + q(t) f(x(σ (t))) = 0 is investigated in this paper, where y(t) = x(t) + p(t)x(?(t)), and ? > 0 is any quotient of odd integers. Using a new method, we obtain some sufficient conditions for the oscillation of the above equation, and some known oscillation criteria be extended. An example is inserted to illustrate the result.

Słowa kluczowe

EN

oscillation; third-order equations; nonlinear; neutral differential equation; eventually positive solution

PL

oscylacja; równanie różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2011
• Tom: Vol. 17, nr 2
• Strony: 155--163
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Zhong J.

autor

Ouyang Z.

autor

Zou S.

• Center of Nuclear Energy Economy and Management, University of South China, Hengyang 421001, P. R. China

Bibliografia

• [1] R. P. Agarwal, S.L. Shang and C. C. Yeh, Oscillation criteria for second-order retarded differential equation, Math. Comput. Modelling 26 (1997), 1-11.
• [2] J. L. Chern, W. C. Lian and C. C. Yeh, Oscillation criteria for second order half-linear differential equations with functional arguments, Publ. Math. Debrecen 48 (1996), 209-216.
• [3] J. Dzurina and I. P. Stavroulakis, Oscillation criteria for second-order delay differential equations, Appl. Math. Comput. 140 (2003), 445^t53.
• [4] S. R. Grace et al.. On the oscillation of certain third order nonlinear functional differential equations, Appl. Math. Comput. 202 (2008), 102-112.
• [5] I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991.
• [6] T. Kusano and Y. Naito, Nonoscillation theorems for a class of quasilinear differential equations of second order, J. Math. Anal. Appl. 189 (1995), 115-127.
• [7] T. Kusano and Y. Naito, Oscillation and nonoscillation criteria for second order quasilinear differential equations, Acta Math. Hungar. 76 (1997), 81-99.
• [8] T. Kusano, Y. Naito and A. Ogata, Strong oscillation and nonoscillation of quasilinear differential equations of second order, Differ. Equ. Dyn. Syst. 2 (1994), 1-10.
• [9] W. T. Li and S. S. Cheng, An oscillation criterion for nonhomogeneous half-linear differential equations, Appl. Math. Lett. 15 (2002), 259-263.
• [10] W. T. Li and P. H. Zhao, Oscillation theorems for second-order nonlinear differential equations with damped term. Math. Comput. Modelling 39 (2004), 457-471.
• [11] D. D. Mirzov, On the oscillation of solutions of a system of differential equations, Mat. Zametki 23 (1978), 401-404.
• [12] C. G. Philos, On the existence of nonoscillatory solutions tending to zero at co for differential equations with positive delays. Arch. Math. 36 (1981), 168-178.
• [13] Y. G. Sun and F. W. Meng, Oscillation of second-order delay differential equations with mixed nonlinearities, Appl. Math. Comput. 207 (2009), 135-139.
• [14] Z. W. Zheng, X. Wang and H. M. Han, Oscillation criteria for forced second order differential equations with mixed nonlinearities, Appl. Math. Lett. 22 (2009), 1096-1101.