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Article Contents

Oscillation results for second order nonlinear neutral differential equations with delay

• 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 $p_{1}(t), p_{2}(t)$.
Mathematics Subject Classification: 34 C 10, 34 C 15.

 Citation:

•  [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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