关键词: 中立型泛函微分方程, 振动性, 渐近性

Abstract: In 1993, J.Wiener brought up an open problem for the study of oscillatory and asympototic properties of neutral functional differential equations with piecewise constant argument ［λt/h］h. The present paper aims at studying these properties of solutions of nonlinear neutral functional differential equation (y(t)+a(t)y(t-1))′+p(t)f(y(［t］))=h(t)，t>=0and giving a sufficient condition for the existence of nonoscillating solutionsof linear equation (y(t)+a(t)y(t-1))′+p(t)y(［t］)=h(t)，t>=0by means of fixed point theory in the case of λ=h=1, where ［·］ is the greatestinteger function.

Key words: neutral functional differential equation, oscillation, asympototic solution