Splitting of systems of differential equations with slowly varying coefficients and irregular singular point (Q1073242)

By using methods of Wasow it is proved that under suitable conditions the system \(\epsilon^{\beta}dx/d\tau =\tau^ qf(\tau,x,\epsilon),\) \(\beta\), q positive integers, has for \(\tau\) large enough a holomorphic solution with asymptotic expansions \(u(\tau,\epsilon)=\sum^{\infty}_{k=1}\tau^{-k}u_ k(\epsilon)\), \(u_ k(\epsilon)=\sum^{\infty}_{j=0}\epsilon^ ju_{k,j}\). The result is used for the splitting of systems of the form \(dx/dt=(\epsilon^{\beta}t)^ qA(\epsilon^{\beta}t,\epsilon)x\) considered in previous work.