Asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients (Q1910016)

This paper considers the neutral differential equation with positive and negative coefficients \([x(t) - C(t) x(t - x)]' + P(t) x(t - \tau) - Q(t) x(t - \sigma) = 0\), \(t \geq t_0\) where \(C,P,Q \in C ([t_0, \infty), \mathbb{R}^+)\), \(r > 0\), \(\tau, \sigma \geq 0\). Sufficient conditions are obtained under which every solution of this equation tends to a constant as \(t \to \infty\). Some results in [\textit{G. Ladas}, \textit{Y. G. Sficas} and \textit{I. P. Stavronlakis}, Proc. Am. Math. Soc. 88, 247-253 (1983; Zbl 0521.34070)] and [\textit{G. Ladas} and \textit{Y. G. Sficas}, Hiroshima Math. J. 18, 351-359 (1988; Zbl 0655.34063)] are improved.