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Existence of nonoscillatory solution of second order neutral differential equation
by Gong Weiming   Cheng Jinfa   Chu Yuming

Vol. 2 No. 3 (2007) P.785~P.795

ABSTRACT

Consider the neutral delay differential equation with positive and negative coefficients:
$(r(t)(x(t) + px(t - \gamma)')' + Q_1(t)x(t-\sigma_1) - Q_2(t)x(t - \sigma_{2}) = 0,$
where $p \in R$ and $\gamma \in (0,\infty), \sigma_1, \sigma_2 \in [0,\infty)$ and $Q_1(t), Q_2(t), r(t) \in C([t_0, \infty),R^+)$ .
Some sufficient conditions for the existence of a nonoscillatory solution of the above equation in terms of $\int^\infty R(s)Q_ids < \infty, i = 1, 2$ are obtained.

KEYWORDS

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 39A10, 34K11, 34K40

MILESTONES