Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations

Year 2013, Volume: 42 Issue: 2, 131 - 138, 01.02.2013

Tongxing Li Shurong Sun Zhenlai Han Bangxian Han - - Yibing Sun

Abstract

In this paper, some new oscillation criteria are obtained for the secondorder quasi-linear neutral delay differential equationr(t)| x(t) + p(t)x(τ (t)) |α−1x(t) + p(t)x(τ (t))+ f t, x(σ(t)) = 0, t ≥ tunder the case when∞ t r α (t) ment some known results in the literature. An example is also providedto illustrate the main results.

Keywords

Oscillation, Neutral delay differential equation, Second-order

Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations

Abstract

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Keywords

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References

• J. K. Hale, Theory of Functional Differential Equations, Spring-Verlag, New York, 1977. R. P. Agarwal, S. L. Shieh, C. C. Yeh, Oscillation criteria for second order retarded differential equations, Math. Comput. Modelling 26, 1–11, 1997.
• J. L. Chern, W. Ch. Lian, C. C. Yeh, Oscillation criteria for second order half-linear differential equations with functional arguments, Publ. Math. Debrecen 48, 209–216, 1996. J. Dˇ zurina, I. P. Stavroulakis, Oscillation criteria for second-order delay differential equations, Appl. Math. Comput. 140, 445–453, 2003.
• T. Kusano, N. Yoshida, Nonoscillation theorems for a class of quasilinear differential equations of second-order, J. Math. Anal. Appl. 189, 115–127, 1995.
• T. Kusano, Y. Naito, Oscillation and nonoscillation criteria for second order quasilinear differential equations, Acta Math. Hungar. 76, 81–99, 1997.
• D. D. Mirzov, On the oscillation of solutions of a system of differential equations, Math. Zametki 23, 401–404, 1978.
• J. Dˇ zurina, D. Hud´ akov´ a, Oscillation of second order neutral delay differential equations, Math. Bohem. 134, 31–38, 2009.
• B. Bacul´ıkov´ a, D. Lackov´ a, Oscillation criteria for second order retarded differential equations, Studies of the University of Zilina, Mathematical Series. 20, 11–18, 2006.
• B. Bacul´ıkov´ a, J. Dˇ zurina, Oscillation of third-order neutral differential equations, Math. Comput. Modelling 52, 215–226, 2010.
• L. Liu, Y. Bai, New oscillation criteria for second-order nonlinear neutral delay differential equations, J. Comput. Math. Appl. 231, 657–663, 2009.
• R. Xu, F. Meng, Some new oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput. 182, 797–803, 2006.
• J. G. Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Comput. Math. Appl. 59, 3710–3717, 2010.
• L. H. Ye, Z. T. Xu, Oscillation criteria for second-order quasilinear neutral delay differential equations, Appl. Math. Comput. 207, 388–396, 2009.
• Z. Han, T. Li, S. Sun, Y. Sun, Remarks on the paper [Appl. Math. Comput. 207 (2009) 388–396], Appl. Math. Comput. 215, 3998–4007, 2010.
• Z. Han, T. Li, S. Sun, W. Chen, On the oscillation of second-order neutral delay differential equations, Adv. Differ. Equ. 2010, 1–8, 2010.
• Z. Han, T. Li, S. Sun, W. Chen, Oscillation criteria for second-order nonlinear neutral delay differential equations, Adv. Differ. Equ. 2010, 1–23, 2010.
• T. Li, Z. Han, P. Zhao, S. Sun, Oscillation of even-order neutral delay differential equations, Adv. Differ. Equ. 2010, 1–9, 2010.
• Z. Han, T. Li, S. Sun, W. Chen, Oscillation of second order quasilinear neutral delay differential equations, J. Appl. Math. Comput. 40, 143–152, 2012.
• T. Li, Z. Han, C. Zhang, S. Sun, On the oscillation of second-order Emden-Fowler neutral differential equations, J. Appl. Math. Comput. 37, 601–610, 2011.
• S. Sun, T. Li, Z. Han, Y. Sun, Oscillation of second-order neutral functional differential equations with mixed nonlinearities, Abstr. Appl. Anal. 2011 1–15, 2011.