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Unboundedness of solutions of a class of planar Hamiltonian systems
Author(s) -
Yang Xiaojing,
Lo Kueiming
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410557
Subject(s) - mathematics , planar , symplectic geometry , hamiltonian (control theory) , hamiltonian system , class (philosophy) , pure mathematics , mathematical physics , matrix (chemical analysis) , combinatorics , mathematical analysis , chemistry , philosophy , computer science , mathematical optimization , computer graphics (images) , epistemology , chromatography
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)