Asymptotic estimation for some nonlinear delay differential equations (Q927807)

Asymptotic properties of solutions of the nonlinear delay differential equation \[ y'(t)+a(t)y(t)= f(t,y(\tau(t))), \quad t\in I= [t_0,\infty) \tag{*} \] are investigated, where \(a,f\) are continuous functions on \(I\) and \(I\times {\mathbb R}\) respectively, \(\tau\) is a real continuous, increasing and unbounded function on \(I\) such that \(\tau (t) < t\) for all \(t> t_0\) and \(\tau (t_0) \leq t_0\). Under further assumptions on the growth of \(f\), some comparison results are obtained and applied to particular cases of (*).