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Oscillation Results for Second Order Nonlinear Differential Equation with Delay and Advanced Arguments

Ethiraju Thandapani|Srinivasan Selvarangam|Murugesan Vijaya|Renu Rama
경북대학교 자연과학대학 수학과|2016.03|Kyungpook Mathematical Journal|제56권 제1호|pp. 137-146

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키워드

NonlinearOscillationSecond orderDifferential equationDelay and advanced argument.
주제분류수학

초록

In this paper we study theoscillation criteria for the second order nonlinear differentialequation with delay and advanced arguments of the form\begin{equation*}\left(\left[x(t)+a(t)x(t-\sigma_1)+b(t)x(t+\sigma_2)\right]^\alpha\right)''+q(t)x^\beta(t-\tau_1)+p(t)x^\gamma(t+\tau_2)=0,~t\geq t_0\end{equation*}where $\sigma_1,~\sigma_2,~\tau_1$ and $\tau_2$ are nonnegativeconstants and $\alpha,~\beta$ and $\gamma$ are the ratios of oddpositive integers. Examples are provided to illustrate the mainresults.

Abstract

In this paper we study theoscillation criteria for the second order nonlinear differentialequation with delay and advanced arguments of the form\begin{equation*}\left(\left[x(t)+a(t)x(t-\sigma_1)+b(t)x(t+\sigma_2)\right]^\alpha\right)''+q(t)x^\beta(t-\tau_1)+p(t)x^\gamma(t+\tau_2)=0,~t\geq t_0\end{equation*}where $\sigma_1,~\sigma_2,~\tau_1$ and $\tau_2$ are nonnegativeconstants and $\alpha,~\beta$ and $\gamma$ are the ratios of oddpositive integers. Examples are provided to illustrate the mainresults.

참고문헌 (23)

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