中立型泛函微分方程解的振动性

Oscillatory Properties of Solutions of Neutral Functional Differential Equations

就λ＝ｈ＝１的情形，解答了由Ｊ．

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())=h(t),t0 and giving a sufficient condition for the existence of nonoscillating solutions of linear equation (y(t)+a(t)y(t-1))′+p(t)y()=h(t),t0 by means of fixed point theory in the case of λ=h =1, where is the greatest integer function.