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neutral differential equation; oscillatory (nonoscillatory) solution; quasi derivatives
The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives $L_n[x(t)+(-1)^r P(t) x(g(t))]+\delta Q(t) f(x(h(t))) = 0,$ where $\ n \ge 2,\ r \in \lbrace 1,2\rbrace ,\ $ and $ \delta = \pm 1.$ There are given sufficient conditions for solutions to be either oscillatory or they converge to zero.
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