A class of neutral nonlinear differential equations is studied. Various classifications of their eventually positive solutions are given. Necessary and/or sufficient conditions are then derived for the existence of these eventually positive solutions. The derivations are based on two fixed point theorems as well as the method of successive approximations.

We are interested in comparing the oscillatory and asymptotic properties of the equations $L_n[x\left(t\right)-P\left(t\right)x\left(g\left(t\right)\right)]+\delta f(t,x\left(h\left(t\right)\right))=0$ with those of the equations $M_n[x\left(t\right)-P\left(t\right)x\left(g\left(t\right)\right)]+\delta Q\left(t\right)q\left(x\left(r\left(t\right)\right)\right)=0.$

A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.