Certain methods for construction of asymptotics for the Hill equations

• Date: 1992
• Main Authors: Shishanin, O. E., Шишанин, О. Е.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1992
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7807
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 t...