Some properties of nonoscillating solutions of functional-differential equations of \(n\)th order (Q1820299)

The authors consider a functional-differential equation of nth order \[ ({\mathcal V}_{n-1}(t)({\mathcal V}_{n-2}(t)(...{\mathcal V}_ 1(t)y'...)')')'+f(t,A_ t^ 1y,A^ 2_ t(y),...,A^ m_ t(y))=q(t) \] where \(n\geq 2\), \(m\geq 1\) are integers and \(A^ i_ t: C([t_ 0,\infty),R)\to R,\) \(i=1,2,...,m\) are functionals defined for every \(t\in [t_ 0,\infty)\). Sufficient conditions are found for which all bounded nonoscillatory solutions and all nonoscillatory solutions of the functional differential equation tend to zero for \(t\to \infty\).