Unboundedness of solutions of a class of planar Hamiltonian systems

✍ Scribed by Xiaojing Yang; Kueiming Lo

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 183 KB
• Volume: 280
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200410557

✦ Synopsis

Abstract

In this paper, the unboundedness of solutions for the following planar Hamilton system

Ju ′ = ∇H (u) + h (t)

is discussed, where the function H (u) ∈ C^2^(R^2^, R) is positive for u ≠ 0 and is positively (q, p)‐quasihomogeneous of quasi‐degree pq, where p > 1 and $ 1 \over p $ + $ 1 \over q $ = 1, h: S^1^ → R^2^ with h ∈ L^∞^(0, 2__π__) is 2__π__ ‐periodic and J is the standard symplectic matrix. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)