Oscillation results for second order nonlinear neutral differential equations with delay

Saroj  Panigrahi; Rakhee  Basu

doi:10.3934/proc.2015.0906

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2015, Volume 2015: 906-912. Doi: 10.3934/proc.2015.0906 open access

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Oscillation results for second order nonlinear neutral differential equations with delay

Saroj Panigrahi^1, and
Rakhee Basu^1,

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

Received: August 31, 2014

Revised: March 31, 2015

Published: October 2015

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Abstract

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 $p_{1}(t), p_{2}(t)$.

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Mathematics Subject Classification: 34 C 10, 34 C 15.

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References

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