A class of solutions of a quasilinear differential system with slowly changing parameters (Q914019)

The authors give sufficient conditions under which the system \[ \dot x_ j=\sum^{j}_{k=1}p_{jk}(t,\epsilon)x_ k+f_ j(t,\epsilon,\theta (t,\epsilon))+\nu \sum^{n}_{k=1}q_{ik}(t,\epsilon,\theta (t,\epsilon))x_ k+ \] \[ +\mu \sum^{N}_{s=-N}X_{js}(t,\epsilon,\theta (t,\epsilon),x_ 1,...,x_ n)\exp (is \theta (t,\epsilon)),\quad j=1,...,n \] has a unique particular solution of the form \[ x_ j(t,\epsilon,\theta (t,\epsilon),\nu,\mu)=\sum^{\infty}_{s=- \infty}\phi_{js}(t,\epsilon,\nu,\mu)\exp (is \theta (t,\epsilon)) \] which fulfils given estimates.