The bounded solution of a class of differential-difference equation of advanced type and its asymptotic behavior (Q1177136)

Conditions for existence of bounded solutions of the advanced differential-difference equation \[ \dot y(t)=\sum_{i=0}^ p A_ i(t)y(t+r_ i)+f(t,y(t),y(t+r_ 1),\dots,y(t+r_ p)), \] \(0=r_ 0<r_ 1<\dots<r_ p\), \(y(t)\in\mathbb{R}^ n\), are given. Both cases when \(\int^ \infty\| A_ i(t)\| dt<\infty\) and \(\lim_{t\to\infty}A_ i(t)\) exist are considered.