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Zbl 0844.34078
Shen, J.H.; Yu, J.S.
Asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients. (English)
[J] J. Math. Anal. Appl. 195, No.2, 517-526 (1995). ISSN 0022-247X

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

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K40 Neutral equations
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: asymptotic behavior; neutral differential equation

Citations: Zbl 0521.34070; Zbl 0655.34063

Cited in: Zbl 1054.34128

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