# American Institute of Mathematical Sciences

2015, 2015(special): 906-912. doi: 10.3934/proc.2015.0906

## Oscillation results for second order nonlinear neutral differential equations with delay

 1 School of Mathematics and Statistics, University of Hyderabad, Hyderabad, Telengana- 500 046, India, India

Received  September 2014 Revised  April 2015 Published  November 2015

In this paper, oscillatory and asymptotic behavior of solutions of a class of nonlinear second order neutral differential equations with positive and negative coefficients of the form \begin{eqnarray*} (r_{1}(t)(x(t)+p_{1}(t)x(\tau(t)))^{\prime})^{\prime}+r_{2}(t)(x(t)+p_{2}(t)x(\sigma(t)))^{\prime} \\+p(t)G(x(\alpha(t)))-q(t)H(x(\beta(t)))=0 \end{eqnarray*} and \begin{eqnarray*} (r_{1}(t)(x(t)+p_{1}(t)x(\tau(t)))^{\prime})^{\prime}+r_{2}(t)(x(t)+p_{2}(t)x(\sigma(t)))^{\prime} \\+p(t)G(x(\alpha(t)))-q(t)H(x(\beta(t)))=f(t) \end{eqnarray*} are studied for various ranges of $p_{1}(t), p_{2}(t)$.
Citation: Saroj Panigrahi, Rakhee Basu. Oscillation results for second order nonlinear neutral differential equations with delay. Conference Publications, 2015, 2015 (special) : 906-912. doi: 10.3934/proc.2015.0906
##### References:
 [1] I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equation with Application, Claredon Press, Oxford, (1991). [2] B. Karpuz, J. V. Manjolvić, Ö. Öcalan. Y. Shoukaku, Oscillation criteria for a class of second-order neutral delay differential equations, Appl. Math. Comp., 210, (2009), 303-312. [3] X. Lin, Oscillation of second order nonlinear neutral differential equations, J. Math. Anal. Appl., 309 (2005), 442-452. [4] W. Shi, P. Wang, Oscillation criteria of a class of second order neutral functional differential equations Appl. Math. Comput., 146 (2003), 211-226. [5] E. M. E. Zayed and M. A. El-Moneam, Some oscillation criteria for second order nonlinear functional ordinary differential equations, Acta Math. Sci., 27B(3) (2007), 602-610.

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##### References:
 [1] I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equation with Application, Claredon Press, Oxford, (1991). [2] B. Karpuz, J. V. Manjolvić, Ö. Öcalan. Y. Shoukaku, Oscillation criteria for a class of second-order neutral delay differential equations, Appl. Math. Comp., 210, (2009), 303-312. [3] X. Lin, Oscillation of second order nonlinear neutral differential equations, J. Math. Anal. Appl., 309 (2005), 442-452. [4] W. Shi, P. Wang, Oscillation criteria of a class of second order neutral functional differential equations Appl. Math. Comput., 146 (2003), 211-226. [5] E. M. E. Zayed and M. A. El-Moneam, Some oscillation criteria for second order nonlinear functional ordinary differential equations, Acta Math. Sci., 27B(3) (2007), 602-610.
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