Certain methods for construction of asymptotics for the Hill equations - Shishanin, O. E. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
On the basis of a method considered by A. Nayfeh we find an asymptotic solution of a special form for the Hill equation in a neighborhood of transition curves. Then, by the averaging method and by means of the corrections obtained up to fourth order we study the same differential equation. We show that the second method also leads to the asymptotics obtained.