Lyapunov stability of periodic solutions of the quadratic Newtonian equation

✍ Scribed by Meirong Zhang; Jifeng Chu; Xiong Li

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 180 KB
• Volume: 282
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200610799

✦ Synopsis

Abstract

We will find a positive constant Σ~2~ such that for any 2__π__ ‐periodic function h (t) with zero mean value, the quadratic Newtonian equation x ″ + x^2^ = σ + h (t) will have exactly two 2__π__ ‐periodic solutions with one being unstable and another being twist (and therefore being Lyapunov stable), provided that the parameter σ is bigger than the first bifurcation value and is smaller than the constant Σ~2~. The construction of Σ~2~ is obtained by examining carefully the twist coefficients of periodic solutions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)