Asymptotic behavior of the oscillatory solutions to first order non-autonomous linear neutral delay differential equations of unstable type

This article is concerned with the asymptotic behavior of the oscillatory solutions to a class of first order unstable type linear neutral delay differential equations with variable coefficients and constant delays. A sufficient condition for all oscillatory solutions to tend to zero at ∞ is established. This condition considerably improves a previous one given by Ladas and the third author [G. Ladas, Y.G. Sficas, Asymptotic behavior of oscillatory solutions, Hiroshima Math. J. 18 (1988) 351–359].